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# A cube with a surface area of 384 $4140_w47_h16.png$ 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?

Question:

A
402 $8865_w47_h16.png$

Explaination

The surface area of a cube is $7942_w23_h16.png$, where *s* is the side length of the cube. So, $8805_w74_h17.png$ gives 8 = s.

The volume of a cube is $1332_w14_h16.png$, so the cube's volume is $5271_w67_h17.png$.

The volume of a square pyramid is $8239_w35_h37.png$, where *B* is the area of the square base and *h* is the height, so the pyramid's volume is $4481_w106_h37.png$.

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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