Geometry - Additional Questions: Sheet 1

Transcription

1 Geometry - Additional Questions: Sheet 1 Parallel Lines Eercises (G3E) e g f h L1 L1 L2 1.) How many angles do you need to know in order to replace the letters in the diagram to the left? b c a d L2 2.) If <a = 115, find the rest of the remaining angles. 132 L3 L4 3.) If L3 and L4 are parallel, what must < equal? 4.) If two lines are truly parallel, what will they never do? *Hint: t Think about intersecting ti lines*

2 Geometry - Additional Questions: Sheet 1 Answers Parallel Lines Eercises (G3E) e g f h L1 L1 L2 1.) How many angles do you need to know in order to replace the letters in the diagram to the left? b c a d L2 Answer: Only 1 angle. 2.) If <a = 115, find the rest of the remaining angles. Answer: <b = <d = <e = <h = 65, <a = <c = <f = <g = L3 L4 3.) If L3 and L4 are parallel, what must < equal? Answer: If L3 and L4 are parallel, < and 132 must add up to 180, therefore < = = 48 4.) If two lines are truly parallel, what will they never do? *Hint: t Think about intersecting ti lines* Answer: Two parallel lines will never touch.

3 Geometry - Additional Eercises: Sheet 2 Additional Shapes and Angles (G4E) Note: The interior angles of any polygon add up to the number of sides the shape has - 2 and then multiplied by 180. E. Triangles have 3 sides --> (3-2) times 180 = 180 E. Rectangles have 4 sides --> (4-2) times 180 = 360 Verte 1.) The reasoning behind this trick all comes back to triangles. How many degrees does a triangle's interior angles add up to? 2.) Now how many triangles can we break up this octagon into from a single verte? *Note: A verte is just a corner made by two lines!* f g h 95 i j 100 l 3.) With the help of this trick, find the remaining angles in the diagram to the left. a b d c 85 o n p

4 Geometry - Additional Eercises: Sheet 2 Answers Additional Shapes and Angles (G4E) Note: The interior angles of any polygon add up to the number of sides the shape has - 2 and then multiplied by 180. E. Triangles have 3 sides --> (3-2) times 180 = 180 E. Rectangles have 4 sides --> (4-2) times 180 = ) The reasoning behind this trick all comes back to triangles. How many degrees does a triangle's interior angles add up to? Verte Answer: ) Now how many triangles can we break up this octagon into from a single verte? *Note: A verte is just a corner made by two lines!* f g h 95 i j 100 l Answer: 6 triangles 3.) With the help of this trick, find the remaining angles in the diagram to the left. a b d c 85 o n p Answer: a = c = 80 b = d = 100 f = h = 85 g = 95 i = l = 80 j = 100 n = o = 95 p = 85

5 Geometry - Additional Eercises: Sheet 3 Triangle Eercises (G5E & G6E) - Find the unknowns, and y y y 60 y A B y 119 Assume that the two triangles to the left are similar. Using this knowledge, find the unknown lengths.

6 Geometry - Additional Eercises: Sheet 3 Answers Triangle Eercises (G5E & G6E) - Find the unknowns, and y = 4.03 = = y y = 8.66, y = 10 = 35.36, y = = 28.8, y = y 340 A B y 119 Assume that the two triangles to the left are similar. Using this knowledge, find the unknown lengths. = , y = 90.62

7 Geometry - Additional Questions: Sheet 4 Perimeters and Circumferences (G7E & G10E) Identify the figures and calculate their perimeters. Be sure to 1.48 m 78 km 111 o 69 o 1104 mm 78 km 69 o 111 o 100 o 80 o km 63 o 80 o 100 o 8.32 yd 8.32 yd 105,600 ft 117 o 11.4 mi 117 o 63 o 30 o 700 ft d = 460,689 light years

8 Geometry - Additional Questions: Sheet 4 Answers Perimeters and Circumferences (G7E & G10E) Identify the figures and calculate their perimeters. Be sure to 1.48 m 78 km 111 o 69 o 1104 mm 78 km Square, P = 312 km 69 o 111 o Parallelogram, P = m = 5168mm 100 o 80 o km 63 o 80 o 100 o 8.32 yd 8.32 yd 105,600 ft 117 o 11.4 mi 117 o 63 o Rhombus, P = yd Trapezoid, P = km = 58.2 mi = 307,296 ft 30 o 700 ft d = 460,689 light years Circle, C = 460,689π ly = 1,447,297.2 ly Circle, C = ft

9 Geometry - Additional Questions: Sheet 5 Areas (G8E & G9E) - Calculate the areas of the figures below. Be sure to treat units appropriately! 15 ft 9' 2" 15 ft 4' 11" 25 m 60 o 19.2 km 24 mi 30 o 60 o 60 o 13 9/12 ft 347 yd 80 o 100 o 120 o 120 o 73 yd 13 9/12 ft 60 o 60 o 100 o yd o 3.75 ft 2.88 ft 92 mm 1.99 ft 3.15 ft 123 mm 51 o

10 Geometry - Additional Questions: Sheet 5 Answers Areas (G8E & G9E) - Calculate the areas of the figures below. Be sure to treat units appropriately! 15 ft 9' 2" 15 ft 4' 11" Square, A = 225 ft 2 Rectangle, A = ft 2 25 m 60 o 19.2 km 24 mi 30 o 60 o 60 o Right triangle, A = mi2 = km2 Triangle, A = m /12 ft 347 yd 80 o 100 o 120 o 120 o 73 yd 13 9/12 ft 60 o 60 o 100 o yd o Rhombus, A = ft 2 Trapezoid, A = 24, yd ft 2.88 ft 3.15 ft 1.99 ft Polygon, A = Insufficient Information 92 mm 51 o 123 mm Triangle, A = 4,397.1 mm 2

11 Geometry - Additional Questions: Sheet 6 Areas of Circles (G11E) - Calculate the areas of the figures below. Be sure to treat units appropriately! D = 5 ft C = 780 mi R = 0.35 mm 60 o 4.3 m 2140 yd 1700 yd

12 Geometry - Additional Questions: Sheet 6 Answers Areas of Circles (G11E) - Calculate the areas of the figures below. Be sure to treat units appropriately! D = 5 ft C = 780 mi A = 19.6 ft 2 A = 48,415 mi 2 R = 0.35 mm 60 o A = mm m A = m 2 A = 1,327,009 yd yd 1700 yd

13 Geometry - Additional Questions: Sheet 7 Surface Areas (G13E) - Calculate the surface areas of the figures below. Be sure to treat units appropriately! R = 5 m 321 mi 15.5 m 476 mi 340 mi R = 30 ft D = 1.92 mm 135 ft 75 ft 2.21 mm 95 ft Note: the cylinder of length 140 ft is centered inside the block.

14 Geometry - Additional Questions: Sheet 7 Answers Surface Areas (G13E) - Calculate the surface areas of the figures below. Be sure to treat units appropriately! R = 5 m 321 mi 15.5 m 476 mi SA = 644 m mi SA = 847,552 mi 2 R = 30 ft D = 1.92 mm 135 ft 75 ft 95 ft Note: the cylinder of length 140 ft is centered inside the block mm SA = mm 2 SA = 68,632.3 ft 2

15 Geometry - Additional Questions: Sheet 8 Surface Area of Cones (G14E) - Find the Base Area, Lateral Area and Total Area of the cones below. 15 in 6.5 mi 4.5 in C = 8.9 mi R = 44 cm H = 700 ft H = 152 cm D = 550 ft

16 TA = 794,272 ft 2 BA = 6,082 cm 2 Geometry - Additional Questions: Sheet 8 Answers Surface Area of Cones (G14E) - Find the Base Area, Lateral Area and Total Area of the cones below. BA = 6.3 mi 2 15 in LA= 28.9 mi 2 TA = 35.2 in mi 4.5 in BA = 63.6 in 2 LA= in 2 TA = in 2 C = 8.9 mi R = 44 cm H = 700 ft BA = 159,043 ft 2 LA= 635,229 ft 2 H = 152 cm LA= 21,874 in 2 D = 550 ft TA = 27,956 cm 2

17 Geometry - Additional Questions: Sheet 9 Surface Area of Spheres (G17E) - Find the Surface Area for the spheres with the dimensions below. 1.) Recall the formula for surface area for a sphere, SA = 4πR 2. If the radious doubled, how much would the SA change? What about if the radius was halved? 2.) R = 35 cm C R 3.) R = 389 mi 4.) D = 12.6 mm 5.) C = 200,209 km 6.) C = 4π ft

18 Geometry - Additional Questions: Sheet 9 Answers Surface Area of Spheres (G17E) - Find the Surface Area for the spheres with the dimensions below. 1.) Recall the formula for surface area for a sphere, SA = 4πR 2. If the radious doubled, how much would the SA change? What about if the radius was halved? Answer: Because the radius is squared, doubling it would cause a 4 increase in surface area. Conversely, halving the radius would result in 4 less surface area. 2.) R = 35 cm SA = 15,394 cm 2 C R 3.) R = 389 mi SA = 1,901,556 mi 2 4.) D = 12.6 mm SA = mm 2 5.) C = 200,209 km SA = 12,759,020,060 km 2 6.) C = 4π ft SA = 50.3 ft 2

19 Geometry - Additional Questions: Sheet 10 Volumes (G17E) - Find the volumes of the figures below. Be mindful of units! 378 in 2.3 m 289 in 7.5 m 255 in 45 ft R = 15 ft 40 ft 19 yd 64 ft 4.5 yd 30 The cylinder of length 65 ft is centered inside the block.

20 Geometry - Additional Questions: Sheet 10 Answers Volumes (G17E) - Find the volumes of the figures below. Be mindful of units! 378 in 2.3 m 289 in 7.5 m 255 in V = 27,856,710 in 3 V = m 3 45 ft R = 15 ft 40 ft 19 yd 64 ft 4.5 yd 30 V = yd 3 The cylinder of length 65 ft is centered inside the block. V = 129,337 ft 3

21 Geometry - Additional Questions: Sheet 11 Volume of Spheres(G16E) - Find the Volume for the spheres with the dimensions below. 1.) Recall the formula for volume of a sphere, V = (4/3)πR 3. If the radious doubled, how much would the V change? What about if the radius was halved? 2.) R = 17 in C R 3.) R = 2.5 mm 4.) D = mi 5.) C = 40 km 6.) C = 2π

22 Geometry - Additional Questions: Sheet 11 Answers Volume of Spheres(G16E) - Find the Volume for the spheres with the dimensions below. 1.) Recall the formula for volume of a sphere, V = (4/3)πR 3. If the radious doubled, how much would the V change? What about if the radius was halved? Answer: Because the radius is cubed, increasing it by a factor of 2 would increase the volume by a factor of 8. Conversely, halving the radius would reduce the volume by a factor of 8. 2.) R = 17 in V = 20,579.5 in 3 C R 3.) R = 2.5 mm 4.) D = 300 mi V = 65.4 mm 3 V = 113,097,336 mi 3 5.) C = 40 km V = 1,039,030 km 3 6.) C = 2π U V = (4/3)π U 3 = 4.19 U 3

23 Geometry - Additional Questions: Sheet 12 Volume of Cones (G16E) - Find the volume of the cones below. R = 4 mm H = 25 m 8.5 mm R = 10 m H = 35.7 in 170 ft Disk area = 25 in 2 C = 55 ft

24 Geometry - Additional Questions: Sheet 12 Answers Volume of Cones (G16E) - Find the volume of the cones below. R = 4 mm H = 25 m 8.5 mm R = 10 m V = 2618 m 3 V = mm 3 H = 35.7 in 170 ft Disk area = 25 in 2 V = in 3 C = 55 ft V = 13,623 ft 3