Study Guide and Review
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- Darrell Lee
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1 State whether each sentence is or false. If false, replace the underlined term to make a sentence. 1. Euclidean geometry deals with a system of points, great circles (lines), and spheres (planes). false, Spherical geometry false, Spherical geometry 2. Similar solids have exactly the same shape, but not necessarily the same size. 3. A right solid has an axis that is also an altitude. false, right cone false, right cone 4. The isometric view is when an object is viewed from a corner. 5. The perpendicular distance from the base of a geometric figure to the opposite vertex, parallel side, or parallel surface is the altitude. 6. Rotation symmetry is also called mirror symmetry. false, reflection false, reflection 7. The intersection of two adjacent lateral faces is the lateral edge. 8. Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate. false, Non-Euclidean geometry false, Non-Euclidean geometry 9. A composite solid is a three-dimensional figure that is composed of simpler figures. 10. The slant height is the height of each lateral face of a pyramid or cone. esolutions Manual - Powered by Cognero Page 1
2 Describe each cross section. 13. CAKE The cake shown is cut in half vertically. Describe the cross section of the cake. 11. A vertical plane containing the vertex of the cone will cut the prism into two parts with a cross section of a triangle. A vertical plane will cut the cake into two parts with a cross section of a rectangle. triangle rectangle Find the lateral area and surface area of each prism. Round to the nearest tenth if necessary. 12. The base of the cylinder is a circle. So, a plane parallel to the base will give a cross section of a circle. 14. circle 78 cm 2 ; 122 cm 2 esolutions Manual - Powered by Cognero Page 2
3 ft 2 ; 202 ft 2 Find the lateral area and surface area of each cylinder. Round to the nearest tenth cm 2 ; cm 2 Find the lateral area and the surface area of each figure. Round to the nearest tenth in 2 ; in 2 36 m 2 ; 45 m 2 esolutions Manual - Powered by Cognero Page 3
4 20. The volume of a cylinder is 770 cm 3. It has a height of 5 cm. Find its radius. 19. Use the Pythagorean Theorem to find the slant height. 7 cm 21. Find the volume of the triangular prism. Find the lateral and surface area cm 2 ; cm cm TRAILERS A semi-truck trailer is basically a rectangular prism. A typical height for the inside of these trailers is 108 inches. If the trailer is 8 feet wide and 20 feet long, what is the volume of the trailer? 1440 ft 3 esolutions Manual - Powered by Cognero Page 4
5 23. Find the volume of a cone that has a radius of 1 cm and a height of 3.4 cm. The volume of a circular cone is, where r is the radius of the base and h is the height of the cone. The radius of the cone is 1 centimeter and the height is 3.4 centimeters. 25. ARCHITECTURE The Great Pyramid measures 756 feet on each side of the base and the height is 481 feet. Find the volume of the pyramid. The volume of a pyramid is, where B is the area of the base and h is the height of the pyramid. The base of the Great Pyramid is a square with sides of 756 feet. It has a height of 481 feet. Therefore, the volume of the cone is about 3.6 cm cm Find the volume of the regular pyramid. Therefore, the volume of the Great Pyramid is 91,636,272 ft 3. 91,636,272 ft 3 Find the surface area of each figure. The volume of a pyramid is, where B is the area of the base and h is the height of the pyramid. The base of this pyramid is a square with a side of 3 centimeters. The height of the pyramid is 6 centimeters. 26. So, the volume of the pyramid is 18 cm in 2 18 cm 3 esolutions Manual - Powered by Cognero Page 5
6 29. sphere: area of great circle = 55π in 2 Find r. 27. Find the volume in 2 Find the volume of each sphere or hemisphere. Round to the nearest tenth. 28. hemisphere: circumference of great circle = 24π m Find r in CONSTRUCTION Cement is poured into a hemisphere that is 6 cm across. What is the volume of cement used? Find the volume cm m 3 esolutions Manual - Powered by Cognero Page 6
7 Name each of the following on sphere A. 33. a triangle containing point B 31. two lines containing point C 34. two lines containing point L C. are lines on sphere A that contain point 32. a segment containing point H L. are lines on sphere A that contain point is a segment on sphere A that contains point H. esolutions Manual - Powered by Cognero Page 7
8 35. a segment containing point J 37. MARBLES Determine whether figure y on the sphere shown is a line in spherical geometry. is a segment on sphere A that contains point J. 36. a triangle containing point K Notice that figure y does not go through the pole of the sphere. Therefore figure y is not a great circle and so not a line in spherical geometry. no Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. 38. Ratio of lengths: Ratio of widths: Ratio of heights: The ratios of the corresponding measures are equal, so the solids are similar. The scale factor is 1:2. Since the scale factor is not 1:1, the solids are not congruent. similar; 1:2 esolutions Manual - Powered by Cognero Page 8
9 42. MODELS A collector s model car is scaled so that 1 inch on the model equals 5 feet on the actual 39. Ratio of radii: Ratio of heights: The ratios of the corresponding measures are equal, so the solids are similar. The scale factor is 1:1. Since the scale factor is 1:1, the solids are congruent. car. If the model is actual car? inches high, how high is the Form a proportion. Let x be the height of the actual car. congruent 40. Ratio of lengths: Ratio of heights: Since the ratios of corresponding measures are not equal, the prisms are neither congruent nor similar. neither 41. Ratio of lengths: Ratio of widths: Since the ratios of corresponding measures are not equal, the prisms are neither congruent nor similar. neither esolutions Manual - Powered by Cognero Page 9
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