Three-Dimensional Geometry
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Question 1 of 14
1. Question
A semicircle with diameter AD = 12cm is rolled to form a cone by connecting A to D. What is the volume of the cone?
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Question 2 of 14
2. Question
A cannonball with a 4-inch radius sinks to the bottom of a barrel full of water, raising the water level by 1/3 of an inch. What is the radius of the cylindrical barrel?
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Question 3 of 14
3. Question
The number of square centimeters in the surface area of a hemisphere (including the base) is equal to the number of cubic centimeters in its volume. What is its radius?
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Question 4 of 14
4. Question
Two cylinders are partially filled with water, each to a depth of 24feet. The smaller cylinder has a radius of 3 feet and the larger has a radius of 4 feet. Water is emptied from the larger cylinder into the smaller cylinder until each holds an equal volume of water. What is the difference between the depths of the two cylinders in feet and inches?
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Question 5 of 14
5. Question
A cone and a hemisphere of equal surface area each have a 3-inch radius. What is the height of the cone?
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Question 6 of 14
6. Question
A cube is inscribed within a hemisphere. The cube has 2-inch edges. What is the surface area of the hemisphere?
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Question 7 of 14
7. Question
A snub cube has 6 squares faces and 32 triangular faces. What is the total number of vertices and edges on a snub cube?
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Question 8 of 14
8. Question
A cylinder with a 6-inch radius is laid on its side and filled to a depth of 9 inches. The cylinder is 24 inches long. What is the volume of water contained in the cylinder?
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Question 9 of 14
9. Question
The radius of a cylinder is increased by 40%, but the height is cut in half. What is the percent change in the volume of the cylinder?
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Question 10 of 14
10. Question
A decagonal trapezohedron has 20 faces, each of which is a kite. How many vertices are there on a decagonal trapezohedron?
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Question 11 of 14
11. Question
A cylinder is inscribed within a sphere. The cylinder has a 6-inch diameter and is 8 inches tall. What is the volume of the sphere?
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Question 12 of 14
12. Question
A cube has a sphere inscribed within and a sphere circumscribed about it. What is the ratio of the surface area of the inscribed sphere to the surface area of the circumscribed sphere?
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Question 13 of 14
13. Question
A wooden cube with 18cm edges has each of the eight corners sliced off so that the resulting faces are equilateral triangles whose edges are 6 cm long. What volume has been removed from the cube? Express your answer in simplest radical form.
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Question 14 of 14
14. Question
How many cubic inches of water are in the rectangular prism, which is tilted at a 30-degree angle?
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