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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?

 Mar 28, 2021
 #1
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The total volume of the sculpture is 17/9.

 Mar 28, 2021
 #2
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That does me no good at all.  How did you get it? 

Guest Mar 28, 2021
 #3
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I knew that something was missing...cheeky 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(32/2 * 3) = 4.5 cubic units

 

Smaller cube   V3 = 33 = 27

 

Larger cube     V4 = 4= 64

 

Total volume    Vt = (27 + 64) - 2(4.5) = 82 cubic units

 Mar 31, 2021

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