Question

A cube is inscribed inside the sphere of diameter 10 cm, it is given that corners of the cube touches the surface of the sphere then, what's the total surface area of the cube?

• A. 1200 $c{m}^2$
• B. 400 $c{m}^2$
• C. 200 $c{m}^2$
• D. 600 $c{m}^2$

Answer 1

The correct option is C 200 $c{m}^2$

Let the length of the side of the cube be $a$ cm.

We know that,
total surface area of cube
$=6(sidelength{)}^2$

Given that,
corners of the cube touches the surface of the sphere.
$\therefore$ diameter of sphere
= length of body diagonal of cube

Now,
applying pythagoras theorem in cube along the body diagonal
$\Rightarrow a^2+(\sqrt{2}a{)}^2={10}^2$
[$(side{)}^2+(sidediagonal{)}^2=(bodydiagonal{)}^2$]
$\Rightarrow 3a^2=100$
$\Rightarrow a^2=\frac{100}{3}$

Hence, total surface area of the cube
= $6a^2$
=$6\times \frac{100}{3}$
= 200 $c{m}^2$