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1212A cube with a surface area of 384 is placed below a square pyramid with a height of 8 units and a side length of 3 units. A student wants to make a model of the combined object that is 25% smaller in volume than the object. What is the volume of the model?

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Question:

A
1212402

explanation

1212The surface area of a cube is , where *s* is the side length of the cube. So, gives 8 = s.

The volume of a cube is , so the cube's volume is .

The volume of a square pyramid is , where *B* is the area of the square base and *h* is the height, so the pyramid's volume is .

The combined volume of the pyramid and cube is 512 + 24 = 536, and 25% smaller than this volume is the same as multiplying the volume by 0.75, which gives 536(0.75) = 402.

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