3. Draw the orthographic projection (front, right, and top) for the following solid. Also, state how many cubic units the volume is.
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1 PAP Geometry Unit 7 Review Name: Leave your answers as exact answers unless otherwise specified. 1. Describe the cross sections made by the intersection of the plane and the solids. Determine if the shape made is similar, congruent, or not similar to the base of the solid. 2. A cube with edges 1 foot long has a cylindrical hole with a diameter of 4 inches drilled through one of its faces. The hole is drilled perpendicular to the face and goes completely through to the other side. Find the surface area and volume of this solid. 3. Draw the orthographic projection (front, right, and top) for the following solid. Also, state how many cubic units the volume is. 4. Determine the volume of the solid with the following orthographic projections. Left Side Top Front
2 4. Which three dimensional figure does the net at the right represent? 5. A snack stand serves a small order of popcorn in a cone-shaped cup and a large order in a cylindrical shaped cup. How much will you have to pay if you buy enough of the small cups of popcorn to equal 6 large orders of popcorn? 6. Find the volume and surface area of the solid. 7. Find the volume and surface area. 30 6b. What happens to the volume, 7b. What would be the volume of this shape if the if you double the radius and the height? if the surface area was increased by 9 times it s current surface area? 8. Assume that you have two solids that are similar (angles all congruent, and ratio of the sides are all congruent). You know the ratio of the sides is 2:5, the surface area of the 1 st solid is 312 cm 2, and the volume of the 2 nd solid is 1000 cm 3. Find the surface area of the 2 nd solid and volume of the 1 st solid.
3 9. Match each of the orthographic projections to the solid on the right. Also, state how many cubic units the volume is. A. B. C. D. E. F. 10. Find the Surface Area, Lateral Area, and Volume of an equilateral triangular prism with the given net? What should change on the net if this were to become a cylinder instead of a triangular prism? Find the volume of the cylinder if the height stays the same, and the width of the rectangle stays the same. 2 ft 12 in
4 11. Form a triangle with the following vertices. (1, 0) (8, 0) (3, 6). If the triangle was rotated around the x-axis, what would be the volume of the resulting figure? 12. A cylindrical glass of water with radius of 2 inches and a height of 10 inches is filled to one inch from the top. If the water is poured from this glass into an inverted cone that has a height of 12 inches, then what is the minimum length for the radius of the cone if the cone is to hold all of the water? Round to the nearest tenth. 13. What is the volume of a regular square pyramid if all the edges are 4 inches long? What would the surface area be? Suppose you have a cube with the same volume what are the dimensions? 14. The following system of equations bounds a region. If this region is rotated about the lines x=0, what is the shape of the resulting solid figure? y = 2x+ 4 x = 0 y = 0 y = 2
5 15. The inverted cone shown has a height of 12 cm and a radius of 6 cm. If water runs into the cone at a rate of 8 cubic centimeters per second, how much time is required to fill the cone? Round to the nearest tenth. 16. A right pentagonal prism has a base with area of 24.8 ft 2 and a height of 6.3 feet. What is the radius of a sphere that has the same volume as the prism? Round to the nearest thousandth. 17. A swimming pool in the shape of a rectangular prism has a length of 23 feet, a width of 16 feet, and a depth of 8 feet. The water level in the pool is exactly 6 feet 4 inches from the bottom. A large object is dropped into the pool causing the water level to rise to exactly 6 feet 7 inches. What is the volume of the object that was dropped into the pool? If that object is a sphere, what would be the radius? Round all answers to the nearest hundredth. 19. You have 2000 cartons of ice cream that come in cube shaped containers with edges of 6 inches. You have to ship the ice cream in a refrigerated truck, and the ice cream must fit in crates that are in the shape of a rectangular prism. A. If the crates are 2.5 feet by 3 feet by 6 feet, how many crates of ice cream are you going to be shipping? B. Suppose that the truck company charges you $15.75 per cubic foot of ice cream that you ship. How much is it going to cost you to ship the ice cream?
6 20. The surface area of a cylinder is 520π. If the surface area is multiplied by 4, by what factor was the volume multiplied? 21. Suppose this square pyramid has a base of 16 in 2, and a slant height of 3 6. Find the lateral surface area, the total surface area, and the volume. 22. Given these two similar solids, the larger hexagonal prism has a surface area 289 cm² and a volume of 4913 cm³, the smaller prism has a volume of 3375 cm³, find the scale factor, and the surface area of the smaller prism.
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