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A pyramid is fitted inside a cube of edge 15 cm so that its base coincides with one face of the cube and its apex touches the centre of the opposite face. What is the volume of this pyramid?

1. 1025 cm^3
2. 1150 cm^3
3. 1225 cm^3
4. 1125 cm^3

Correct answer: 1125 cm^3

Solution

The base is a face of the cube with area 15 x 15 = 225 cm^2, and the height equals the cube edge, 15 cm. Volume = (1/3) x 225 x 15 = 1125 cm^3.

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