Question

A cubical has a total surface are of 100 $m^2$ and the lateral surface area of 50 $m^2$. Find the area of its base.

Answer 1

Total surface area of circle$=100m^2$

$\therefore 6a^2=100$

$\therefore a^2=\frac{100}{6}=\frac{50}{3}$

$a=\sqrt{\frac{50}{3}}$

Lateral surface area $=4a^2=5$

or $a=\frac{5}{\sqrt{2}}$

Area of base$=a\times a$

$=\frac{5}{\sqrt{2}}\times \frac{5}{\sqrt{2}}$

Area of base$=\frac{25}{2}{m}^2$.