A solid sculpture consists of a cube with a cube sticking out, as shown. The vertices of the smaller cube lie on the edges of the large cube, the same distance along each. What is the total volume of the sculpture?

Guest Mar 28, 2021

#3**+3 **

I knew that something was missing... Here's the whole question:

A solid sculpture consists of a 4x4x4 cube with a 3x3x3 cube sticking out, as shown. Three vertices of the smaller cube lie on the edges of the larger cube, the same distance along each.

What is the total volume of the sculpture?

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1/3(3^{2}/2 * 3) = 4.5 cubic units

Smaller cube V_{3} = 3^{3} = 27

Larger cube V_{4} = 4^{3 }= 64

Total volume V_{t} = (27 + 64) - 2(4.5) = 82 cubic units

civonamzuk Mar 31, 2021