Question

The figure given below shows a solid made up of 10 identical cubes. When the solid is painted the total area that is painted is $360c{m}^2$. What is the volume of the solid ?

• A. $80c{m}^3$
• B. $216c{m}^3$
• C. $270c{m}^3$
• D. $2160c{m}^3$

Answer 1

The correct option is C $270c{m}^3$

Let us consider the painted solid surface given below:

Bottom surface $=6$

First layer surface $=16$

Second layer surface $=8$

Third layer surface $=10$

Therefore the total number of painted surface = 40.

Since it is given that the total area of the solid painted is $360c{m}^2,$ therefore,

1 side $=\frac{360c{m}^2}{40}=9c{m}^2$

1 side $=\sqrt{9c{m}^2}=3cm$

Thus, total volume $=3\times 3\times 3\times 10=270c{m}^3$