Question

The diagonal of a cube is 6√3 cm. Find its surface area

A) 216 sq.cm B) 316 sq.cm C) 416 sq.cm D) 516 sq.cm

Answer 1

S O L U T I O N :

We have, the diagonal of a cube is 6√3 cm.

We know that formula of the diagonal of cube :

$\boxed{\bf{Diagonal\:(D)=\sqrt{3} a}}}}$

$\longrightarrow\sf{\sqrt{3}a=6\sqrt{3} }\\\\\longrightarrow\sf{a=\dfrac{6\cancel{\sqrt{3}} }{\cancel{\sqrt{3}} } }\\\\\longrightarrow\bf{a=6\:cm}$

∴ The one side of cube will be a = 6 cm.

We know that formula of the total surface area of cube :

$\boxed{\bf{Total\:surface\:area\:of\:cube=6a^{2}\:\:\:\:(sq.unit) }}}}$

$\longrightarrow\sf{Surface\:area=6\times a\times a}\\\\\longrightarrow\sf{Surface\:area=(6\times 6\times 6)cm^{2} }\\\\\longrightarrow\sf{Surface\:area=(36\times 6)cm^{2} }\\\\\longrightarrow\bf{Surface\:area=216\:cm^{2} }$

Thus;

The total surface area of cube will be 216 cm² .

Option (a)