Question

Dimensions of a cuboid are $25$ cm $\times 20$ cm $\times 4$ cm. The volume of a cube is half the volume of the cuboid. What is the total surface area of such a cube?

• A. $400c{m}^2$
• B. $600c{m}^2$
• C. $800c{m}^2$
• D. $1200c{m}^2$

Answer 1

Answer: (B)

$600c{m}^2$

Volume of the cube $=\frac{1}{2}\times$ volume of cuboid
$=\frac{1}{2}\times (25\times 20\times 4)c{m}^3=1000c{m}^3$

$\therefore$ edge of the cube $=\sqrt[3]{31000}$ cm $=10$ cm
Surface area of the cube $=$ $6\times ($ edge${)}^2$

$=6\times (10{)}^{2}c{m}^2$
$=600c{m}^2$