Illustrative Mathematics - Geometry - Unit 5 - Lesson 15

A right cone has a base with diameter 10 units. The volume of the cone is 100\pi cubic units. What is the length of a segment drawn from the apex to the edge of the circular base?

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A right pyramid has a square base with sides of length 10 units. Each segment connecting the apex to a midpoint of a side of the base has length 13 units. What is the volume of the pyramid?

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A pyramid has a height of 8 inches and a volume of 120 cubic inches. Determine 2 possible shapes, with dimensions, for the base.

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A toy company packages modeling clay in the shape of a rectangular prism with dimensions 6 inches by 1 inch by \frac{1}{2} inch. They want to change the shape to a rectangular pyramid that uses the same amount of clay. Determine 2 sets of possible dimensions for the pyramid.

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These 3 congruent square pyramids can be assembled into a cube with side length 2 feet. What is the volume of each pyramid?

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A monster truck wheel has an area of 324\pi square inches. A toy company wants to create a scaled copy of the monster truck with a wheel area of 9\pi square inches. What scale factor should the company use?

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