Æ. Add a point T on the ray so that. ML. (Lesson 1.3) 20. H(º1, 3) 21. H(3, º1) 22. H(º5, 2) M(1, 7) M(8, 2) M(º4, 6) L(3, 3) L(3, 5) L(º6, 2)

Transcription

1 tra ractice escribe a pattern in the seuence of numbers. redict the net number. (Lesson.).,, 4, 2,,... 2., 2, 4, 7,,....,, 2,, , 2, 2,, 2, 2, 9, 2, 2,.... 2, 4, 72, 0,.... 2, º,, º4, omplete the conjecture based on the pattern ou observe in the specific cases. (Lesson.) onjecture: n negative number cubed is?. º = º º7 = º4 º = º27 º9 = º729 º = º º = º. how that n n + > (n + ) n for the values n =, 4, and. hen show that the values n = and n = 2 are countereamples to the conjecture that n n + > (n + ) n. (Lesson.) ketch the points, lines, segments, planes, and ras. (Lesson.2) 9. raw four collinear points,,, and. 0. raw two opposite ras Æ and Æ.. raw a plane that contains two intersecting lines.. raw three points,, and that are coplanar, but are not collinear.. raw two points, and. hen sketch Æ. dd a point on the ra so that is between and. Æ In the diagram of the collinear points, = 24, is the midpoint of, =, and =. ind each length. (Lesson.) Use the istance ormula to decide whether Æ Æ L. (Lesson.) 20. (º, ) 2. (, º) 22. (º, 2) (, 7) (, 2) (º4, ) L(, ) L(, ) L(º, 2) ame the verte and sides of the angle, then write two names for the angle. (Lesson.4) tra ractice 0

2 Use the ngle ddition ostulate to find the measure of the unknown angle. (Lesson.4) 2. m =? 27. m =? 2. m =? 0 L tate whether the angle appears to be acute, right, obtuse, or straight. hen estimate its measure. (Lesson.4) ind the coordinates of the midpoint of a segment with the given endpoints. (Lesson.) 2. (º4, 2). (º,.) 4. (º, 4) Q(, º4) Q(7, º.) Q(º, º) XY Æ is the angle bisector of UX. ind m UXY. (Lesson.).. 7. U Y (4r ) X Y (r 7) 4 X U (z 9) X (7z ) Y U ind the measure of each angle. (Lesson.). wo vertical angles are complementar. ind the measure of each angle. 9. he measure of one angle of a linear pair is times the measure of the other angle. ind the measures of the two angles. 40. he supplement of an angle is 0. ind the complement of the angle. ind the perimeter (or circumference) and area of the figure. (Where necessar, use π.4.) (Lesson.7) tudent esources

3 2 ewrite the conditional statement in if-then form. (Lesson 2.). It must be true if ou read it in a newspaper. 2. n apple a da keeps the doctor awa.. he suare of an odd number is odd. Write the inverse, converse, and contrapositive of the conditional statement. (Lesson 2.) 4. If =, then 2 = 44.. If ou are indoors, then ou are not caught in a rainstorm.. If four points are collinear, then the are coplanar. 7. If two angles are vertical angles, then the are congruent. Write the converse of the true statement. ecide whether the converse is true or false. If false, provide a countereample. (Lesson 2.). If two angles form a linear pair, then the are supplementar. 9. If 2 º = 7, then =. ewrite the biconditional statement as a conditional statement and its converse. (Lesson 2.2) 0. wo segments have the same length if and onl if the are congruent.. wo angles are right angles if and onl if the are supplementar.. = 0 if and onl if 2 = 00. etermine whether the statement can be combined with its converse to form a true biconditional statement. (Lesson 2.2). If is a right angle, then fi. 4. If and 2 are adjacent, supplementar angles, then and 2 form a linear pair.. If two angles are vertical angles, then the are congruent. Using p,, r, and s below, write the smbolic statement in words. (Lesson 2.) p:we go shopping. :We need a shopping list. r : We stop at the bank. s: We see our friends.. p 7. ~r ~s. r s 9. p 20. ~p ~s 2. p r iven that the statement is of the form p, write p and. hen write the inverse and the contrapositive of p both smbolicall and in words. (Lesson 2.) 22. If it is hot, a will go to the beach. 2. If the hocke team wins the game tonight, the will pla in the championship. 24. If ohn misses the bus, then he will be late for school. tra ractice 0

4 Use the propert to complete the statement. (Lesson 2.4) 2. efleive propert of eualit: =?. 2. mmetric propert of eualit: If =, then?. 27. ransitive propert of eualit: If = and =, then?. 2. ivision propert of eualit: If 2 =, then 2 = z?. 29. ubtraction propert of eualit: If =, then º 4 =?. op and complete the proof using the diagram and the given information. (Lesson 2.) 0. IV Æ Æ, is the midpoint of Æ and Æ Æ Æ OV tatements easons. is the midpoint of Æ and Æ. 2. =. = 4.?. =.? Æ Æ 7..? 2.?.? 4. iven.?. ransitive propert of eualit 7. efinition of congruent segments In ercises 2, use the diagram to complete the statement. (Lesson 2.). 2 and? are vertical angles. 2. QW is supplementar to?.. In the diagram, suppose that and 4 are complementar and that 4 and are complementar. rove that. (Lesson 2.) olve for each variable. (Lesson 2.) V U W (z ) ( 4) (4z ) (0 ) (9b ) (c ) (c 9) (7b 20) (r 44) (s ) (s 9) (r ) 7. Write a two-column proof. (Lesson 2.) IV and 4 are complementar, is a right angle. OV 2 and are complementar tudent esources

5 hink of each segment in the diagram as part of a line. ill in the blank with parallel, skew, or perpendicular. (Lesson.). and are?. 2. and are?.. and are?. hink of each segment in the diagram as part of a line. here ma be more than one right answer. (Lesson.). 4. ame a line parallel to.. ame a line perpendicular to.. ame a line skew to 7. ame a plane parallel to. omplete the statement with corresponding, alternate interior, alternate eterior, or consecutive interior. (Lesson.). and 7 are? angles and are? angles and 2 are? angles.. 4 and are? angles.. and are? angles.. ill in the blanks to complete the proof. (Lesson.2) Æ Æ IV fi, Æ bisects OV m = 4 tatements Æ Æ. fi 2.?. m = Æ bisects. m = m. m + m = m +? = 90. 2(m ) = m = 4 easons.? 2. efinition of perpendicular lines.? 4.?.?.? 7. ubstitution propert of eualit.? 9.? tra ractice 07

6 ind the values of and. plain our reasoning. (Lesson.) Which lines, if an, are parallel? plain. (Lesson.4) plain how ou would show that a b. tate an theorems or postulates that ou would use. (Lesson.) ind the slopes of,, and.which lines are parallel, if an? (Lesson.) 2. (, 7), (, ) 27. (º4, ), (, ) 2. (º, 2), (º, ) (4, ), (9, ) (º2, º), (4, º) (7, º), (7, 7) (2, ), (º, º) (º0, ), (4, º) (4, º), (4, º) Write an euation of the line that passes through point and is parallel to the line with the given euation. (Lesson.) 29. (º4, º), = º 7 0. (2, º), = º + 4. (º9, ), = º 2 ecide whether lines p and p 2 are perpendicular. (Lesson.7) 2. line p : º7 + =. line p : + = 4. line p : º 2 = line p 2 : º9 º 2 = line p 2 : º 2 = 9 line p 2 : º º 2 = Line j is perpendicular to the line with the given euation and line j passes through. Write an euation of line j. (Lesson.7). = º2 +, (4, º). 2 + = 20, (4, 0) 7. = +, (º2, º7) 2 0 tudent esources

7 4 In ercises 4, the variable epressions represent the angle measures of a triangle. ind the measure of each angle. hen classif the triangle b its angles. (Lesson 4.). m = 2. m = 0. m = 4. m = (2) m = m = m Q = (2 + 0) m = (2 º 4) m = m L = m = ( + 0) m U = (2 º 2). he measure of an eterior angle of a right triangle is. ind the measures of the interior angles of the triangle. (Lesson 4.) Identif an figures that can be proved congruent. or those that can be proved congruent, write a congruence statement. (Lesson 4.2) Use the triangles in ercise above. Identif all pairs of congruent corresponding angles and corresponding sides. (Lesson 4.2) Use the given information to find the value of. (Lesson 4.2) 0. Q,.,., 47 V ( 2). none; corresponding sides are congruent, but no information is given about the corresponding angles. 2 L ( ) ecide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate ou would use. (Lesson 4.). XVY, ZVW 4., Q. X V Z Y W. Use the diagram in ercise. rove that XYW ZWY. Is it possible to prove that the triangles are congruent? If so, state the congruence postulate or theorem ou would use. (Lesson 4.4) tra ractice 09

8 Write a two-column proof or a paragraph proof. (Lesson 4.4) 20. IV Æ Æ, Æ Æ bisects OV tate which postulate or theorem ou can use to prove that the triangles are congruent. hen eplain how proving that the triangles are congruent proves the given statement. (Lesson 4.) Æ Æ 2. OV 22. OV 2. OV Q Use the diagram and the information given below. (Lesson 4.) IV 24. OV 2. OV Æ Æ 2. OV Æ Æ ind the values of and. (Lesson 4.) lace the figure in a coordinate plane. Label the vertices and give the coordinates of each verte. (Lesson 4.7) 0. 4 unit b unit rectangle with one verte at (º, 2). suare with side length and one verte at (, º4) In the diagram, is a right triangle. Its base is 0 units and its height is 0 units. (Lesson 4.7) 2. ive the coordinates of points and.. ind the length of the hpotenuse of. lace the figure in a coordinate plane and find the given information. (Lesson 4.7) (0, 20) 4. rectangle with length units and width units; find the length of a diagonal of the rectangle.. n isosceles right triangle with legs of 7 units; find the length of the hpotenuse. 0 tudent esources

9 Use the diagram shown. (Lesson.). In the diagram, Æ fi Æ Æ Æ and. ind. 2. In the diagram, Æ fi Æ Æ Æ and. ind.. In the diagram, Æ is the perpendicular bisector of Æ. ecause = =, what can ou conclude about the point? 20 Use the diagram shown. (Lesson.) 4. In the diagram, m = m = 0, m = m = 90, and =. ind.. In the diagram, Æ bisects, m = m = 90 and = = 0. What can ou conclude about point? In each case, find the indicated measure. (Lesson.2). he perpendicular bisectors of 7. he perpendicular bisectors of meet at point. ind. meet at point. ind. 0. he angle bisectors of 9. he angle bisectors of meet at point Q. ind W. meet at point. ind. 24 W 2 7 X Y 0 2 Use the figure below and the given information. (Lesson.) is the centroid of, = 4, X = 24, and Z =.. Æ. 0. ind the length of Y. ind the length of X Æ. Y Z. ind the length of Æ. X raw and label a large triangle of the given tpe and construct altitudes. Verif heorem. b showing that the lines containing the altitudes are concurrent and label the orthocenter. (Lesson.). an isosceles 4. an euilateral. a right isosceles tra ractice

10 Use, where X, Y, and Z are midpoints of the sides. (Lesson.4) Æ.?. Æ 7. XY?.. If =, then YZ =?. 9. If = 0, then XY =?. 20. If XZ =, then =?. Z X 2. If YZ = 4 º and = +, then YZ =?. Y 22. If Z = 4 º and XY = 2 +, then =?. ame the shortest and longest sides of the triangle. (Lesson.) ame the smallest and largest angles of the triangle. (Lesson.) 2. L omplete with >, <, or =. (Lesson.) 29.? 0. Q? U. m? m U 2.?. m? m 2 4. m? m L ?. XY? WV 7. m? m 2 L U U W 0 9 X V 9 0 Y Z tudent esources

11 ecide whether the figure is a polgon. If it is, use the number of sides to tell what kind of polgon the shape is. hen state whether the polgon is conve or concave. (Lesson.) Use the information in the diagram to solve for. (Lesson.) ( ) 0 ( ) 70 (4 0) (7 ) (7 ) ( 2) () 02 Use the diagram of parallelogram VWXY at the right. omplete each statement, and give a reason for our answer. (Lesson.2) 0. VW Æ?. VWX? V W. Æ XW?. V Æ? 4. XYW? Æ. WX?. VYX is supplementar to? and?. 7. oint is the midpoint of? and?. Y X re ou given enough information to determine whether the uadrilateral is a parallelogram? plain. (Lesson.) rove that the points represent the vertices of a parallelogram. (Lesson.) 2. (2, 4), (4, º), (9, º), (7, ) 22. (º7, º), (º, º2), (º4, º9), (º0, º) 2. (º, ), (, 4), (2, º), U(º9, º4) 24. (º7, º), (, 0), (, 4), Q(º, º9) tra ractice

12 List each uadrilateral for which the statement is true. (Lesson.4) 2. djacent angles are supplementar. 2. djacent angles are congruent. 27. djacent sides are perpendicular. 2. iagonals are congruent. 29. djacent sides are congruent. 0. Opposite sides are parallel. It is given that Q is a parallelogram. raph Q. ecide whether it is a rectangle, a rhombus, a suare, or none of the above. ustif our answer using theorems about uadrilaterals. (Lesson.4). (, 7), Q(º2, ), (, º), (4, ) 2. (º, ), Q(4, ), (7, 7), (º, ). (º2, 7), Q(4, 7), (4, ), (º2, ) 4. (º7, º2), Q(º2, º2), (º2, º7), (º7, º7) ind the missing angle measures. (Lesson.) U ind the value of. (Lesson.) What are the lengths of the sides of the kite? (Lesson.) What kind of uadrilateral could be? is not drawn to scale. (Lesson.) ind the area of the polgon. (Lesson.7) tudent esources

13 7 Use the graph of the transformation below. (Lesson 7.). ame the image of Q. 2. ame and describe the transformation.. ame two sides with the same length. 4. ame two angles with the same measure. Z 4 Y. ame the coordinates of the preimage of point Y. X. how two corresponding sides have the same length, using the istance ormula. œ ame and describe the transformation. hen name the coordinates of the vertices of the image. (Lesson 7.) 7.. L œ Use the diagrams to complete the statement. (Lesson 7.) ? 0.?.? Use the diagram at the right to name the image of after the reflection. If the reflection does not appear in the diagram, write not shown. (Lesson 7.2). eflection in the -ais. eflection in the -ais 4. eflection in the line =. eflection in the -ais, followed b a reflection in the -ais ind the coordinates of the reflection without using a coordinate plane. hen check our answer b plotting the image and preimage on a coordinate plane. (Lesson 7.2). (, 2) reflected in the -ais 7. (º2, 4) reflected in the -ais. (, º) reflected in the -ais 9. Q(, ) reflected in the -ais tra ractice

14 ind point on the -ais so + is a minimum. (Lesson 7.2) 20. (, 2), (, ) 2. (, 7), (, 7) 22. (º2, 7), (º9, ) ame the coordinates of the vertices of the image after a clockwise rotation of the given number of degrees about the origin. (Lesson 7.) O O 4 O In the diagram, a b, is reflected in line a and is reflected in line b. (Lesson 7.4) a b 2. translation of maps onto which triangle?? 27. Which lines are perpendicular to fl. 2. ame two segments parallel to fl op figure V and draw its image after the translation. hen describe the translation using a vector in component form. (Lesson 7.4) 29. (, ) ( º, + ) 0. (, ) ( +, º 4). (, ) ( º 7, + 7) 2. (, ) ( + 2, º ) ketch the image of (º, º2) after the described glide reflection. (Lesson 7.). ranslation: (, ) ( +, + ) 4. ranslation: (, ) ( + 4, º ) eflection: in the -ais eflection: in = º4 ketch the image of after a composition using the given transformations in the order the appear. (Lesson 7.). (, ), (º2, ), (º, º4). (2, ), (0,º), (º, º4) ranslation: (, ) ( º 7, ) ranslation: (, ) ( +, ) eflection: in the -ais eflection: in the -ais escribe each frieze pattern according to the following seven categories:,,, V,, V, and V. (Lesson 7.) 7.. V tudent esources

15 ewrite the fraction so that the numerator and denominator have the same units. hen simplif. (Lesson.) m. 2. f 2 0 cm 4 t d. 2 in. ft 4. 0 km 9 00 m Use ratios to solve the following problems. (Lesson.). he measures of the angles in a uadrilateral are in the etended ratio of :4::. ind the measures of the angles.. he perimeter of isosceles triangle is cm. he etended ratio of :: is ::. ind the lengths of the three sides. olve the proportion. (Lesson.) a 7. = 2. º = º 2 c = b º = 2 2. = f º. = g + d + º 9 9 g º 4 omplete the sentence. (Lesson.2). If = 0, then =? 0 0?. 4. If 9 4 =, then =? 4?.. If 9 = 2, then 4 =??.. If z z + =, then =??. ind the geometric mean of the two numbers. (Lesson.2) 7. 4 and 9. and and and 2. 2 and and 0,000 Use the diagram and the given information to find the unknown length. (Lesson.2) 2. IV =, find. 24. IV Q =, find In the diagram, Q ~ VWX. (Lesson.) 2. ind the scale factor of Q to VWX. 2. ind the scale factor of VWX to Q. 27. ind the values of u,, and z. 2. ind the perimeter of each polgon. 9 u X z V W tra ractice 7

16 etermine whether the triangles can be proved similar. If the are similar, write a similarit statement. If the are not similar, eplain wh. (Lesson.4) U V 0 ind coordinates for point Z so that OWX ~ OYZ. (Lesson.4) 2. O(0, 0), W(4, 0), X(0, ), Y(, 0). O(0, 0), W(2, 0), X(0, ), Y(, 0) 4. O(0, 0), W(º4, 0), X(0, 2), Y(º, 0). O(0, 0), W(º, 0), X(0, º4), Y(º, 0) re the triangles similar? If so, state the similarit and the postulate or theorem that justifies our answer. (Lesson.) etermine whether the triangles are similar. If the are, write a similarit statement and solve for the variable. (Lesson.) etermine whether the given information implies that Q Æ Æ. plain. (Lesson.) U 2 20 V ind the value of the variable. (Lesson.) Use the origin as the center of the dilation and the given scale factor to find the coordinates of the vertices of the image of the polgon. (Lesson.7) 4. (º2, ), (º, ), (, ), (2, º4), k = (2, 0), (, ), (4, ), (, ), k = 4. (, º), (, º), (, 9), (º, 9), k = 49. (4, º4), (, 4), (2, ), (º, º4), k = 4 tudent esources

17 9 Write similarit statements for the three similar triangles in the diagram. hen complete the proportion. (Lesson 9.). =? 2.? =. =? L ind the value of the variable. (Lesson 9.) U V ind the unknown side length. implif answers that are radicals. ell whether the side lengths form a thagorean triple. (Lesson 9.2) V U he variables r and s represent the lengths of the legs of a right triangle, and t represents the length of the hpotenuse. he values of r, s, and t form a thagorean riple. ind the unknown value. (Lesson 9.2) 0. r = 7, t = 2. r =, s =. s = 2, t =. r = 49, s = 4. s = 9, t = 202. r = 2, t = ind the area of the figure. ound decimal answers to the nearest tenth. (Lesson 9.2). cm 7.. cm cm cm cm 9 cm 9 cm L 4 cm ell whether the triangle is a right triangle. (Lesson 9.) 9. U X Z 2 Y tra ractice 9

18 ecide whether the numbers can represent the side lengths of a triangle. If the can, classif the triangle as right, acute, or obtuse. (Lesson 9.) 22. 7,, 9 2.,, 9 24.,, 2. 7, 9, 2. 00, 00, ,, 20 ind the value of each variable. Write answers in simplest radical form. (Lesson 9.4) ind the sine, the cosine, and the tangent of the acute angles of the triangle. press each value as a decimal rounded to four places. (Lesson 9.). 2. U 4 V. Y W X 29 Z ind the value of each variable. ound decimals to the nearest tenth. (Lesson 9.) 4... u v 42 w z 7 olve the right triangle. ound decimals to the nearest tenth. (Lesson 9.) raw vector Q Æ in a coordinate plane. Write the component form of the vector and find its magnitude. ound our answer to the nearest tenth. (Lesson 9.7) 40. (2, ), Q(, 7) 4. (º, º), Q(, ) 42. (º4, ), Q(2, º) Let a =,, b = º7, 2, c =, º, and d = 2, 9. ind the given sum. (Lesson 9.7) 4. a + b 44. a + c 4. c + d 4. b + c 20 tudent esources

19 0 atch the notation with the term that best describes it. (Lesson 0.) Æ.. ecant 2.. hord.. adius Æ 4.. iameter.. oint of tangenc.. ommon eternal tangent 7.. ommon internal tangent. Æ. enter ell whether the common tangent(s) are internal or eternal. (Lesson 0.) Use the diagram at the right. (Lesson 0.). What are the center and radius of?. What are the center and radius of? 4. escribe the intersection of the two circles.. escribe all the common tangents of the two circles. Æ Æ and are diameters. op the diagram. ind the indicated measure. (Lesson 0.2). m 7. m. m 9. m 20. m Q 2. m Q 22. m 2. m ind the value of each variable. (Lesson 0.) tra ractice 2

20 ind the value of. (Lesson 0.4) ind the value of. (Lesson 0.) ive the center and radius of the circle. (Lesson 0.) 9. ( º ) 2 + ( + ) 2 = ( + ) = ( +.) 2 + ( º 4.9) 2 = ( º ) 2 + ( + 7) 2 = Write the standard euation of the circle with the given center and radius. (Lesson 0.) 4. center (, ), radius 44. center ( 2, 7), radius 0 Use the given information to write the standard euation of the circle. (Lesson 0.) 4. he center is (2, 2); a point on the circle is (2, 0). 4. he center is (0, ); a point on the circle is (º, ). Use the graph at the right to write euation(s) for the locus of points in the coordinate plane that satisf the given condition. (Lesson 0.7) 47. euidistant from and 4. units from units from 0. units from 22 tudent esources

21 ind the sum of the measures of the interior angles of the conve polgon. (Lesson.). -gon 2. 4-gon. 0-gon gon ind the value of. (Lesson.) You are given the number of sides of a regular polgon. ind the measure of each eterior angle. (Lesson.) You are given the measure of each eterior angle of a regular n-gon. ind the value of n. (Lesson.) ind the measure of a central angle of a regular polgon with the given number of sides. (Lesson.2). 0 sides 7. sides. 2 sides sides ind the perimeter and area of the regular polgon. (Lesson.2) In ercises 2 2, the polgons are similar. ind the ratio (red to blue) of their perimeters and of their areas. (Lesson.) he ratio of the perimeters of two similar heagons is :. he area of the larger heagon is 20 suare inches. What is the area of the smaller heagon? (Lesson.) tra ractice 2

22 ind the indicated measure. (Lesson.4) 0. ircumference. adius r r in. r 7 ft ind the indicated measure. (Lesson.4) 2. Length of. ircumference 4. adius V U. Length of. ircumference 7. adius ind the area of the shaded region. (Lesson.) ind the probabilit that a point, selected randonl on Æ,is on the given segment. (Lesson.) Æ Æ Æ 4. ind the probabilit that a randoml chosen point in the figure lies in the shaded region. (Lesson.) Æ tudent esources

23 ell whether the solid is a polhedron. If it is, decide whether it is regular and/or conve. plain. (Lesson.). 2.. ount the number of faces, vertices, and edges of the polhedron. Verif our results using uler s heorem. (Lesson.) 4... escribe the cross section. (Lesson.) 7.. ind the surface area of the right prism. (Lesson.2) cm. 4 cm in. cm cm 0 cm in. 2 in. ind the surface area of the right clinder. ound the result to two decimal places. (Lesson.2). in.. cm 4. in. cm ind the surface area of the solid. he pramids are regular and the cone is right. (Lesson.). in.. rea 9. cm 2 7. cm in. cm in. cm cm tra ractice 2

24 about 9. cm ind the volume of the solid. (Lesson.4). ight rectangular prism 9. ight clinder 20. Obliue suare prism 90 in. about ft 0 cm ft in. ft 20 cm 0 in. in. cm 2. Obliue clinder 22. wo holes are drilled 2. suare hole is cut about in. through a cube. from a clinder. about ft 7 in. in. 2 cm cm ft 4 ft ft cm cm ind the volume of the pramid or cone. (Lesson.) cm cm in. cm cm 9 in. 40 cm 70.4 cm 2 in in. mm 7 in. ft ft 7. mm about. in. about.7 mm about 7.27 ft ind the surface area and the volume of the sphere. ound our result to two decimal places. (Lesson.) m cm in cm 2 ; 244. cm 2.72 m 2 ; m in. 2 ; 24, in. he solid is similar to a larger solid with the given scale factor. ind the surface area and volume V of the larger solid. (Lesson.7). cale factor 2: 4. cale factor :. cale factor :7 = 9 m 2 V = 4 m = 04π ft 2 V = 44π ft = 00π cm 2 V = 2 π cm 2 m 2 ; 2 m about 2.9π ft 2 ; about.7π ft ; 9π cm 2 ; 47} }π cm 2 tudent esources