Question

if the length of the diagonal of a cube is 8√3 find its total surface area.​

Answer 1

◆ Question ◆

if the length of the diagonal of a cube is 8√3 find its total surface area.

$\rule{300}2$

Length of the diagonal =8√3a

= a√3=8√3

=8cm.

surface area =$6a^{2}$

=6×8×8

=6×64

=384$cm^{2}$

Answer 2

Solution :

Given :

The length of the diagonal of a cube is 8√3.

$\bf{\underline{\bf{Explanation\::}}}}$

We know that formula of the diagonal of cube :

$\boxed{\bf{Diagonal\:of\:cube=\sqrt{3} a}}}}$

A/q

$\longrightarrow\tt{\sqrt{3}a=8\sqrt{3}} \\\\\\\longrightarrow\tt{a=\dfrac{8\cancel{\sqrt{3}} }{\cancel{\sqrt{3}} } }\\\\\\\longrightarrow\bf{a=8\:units}$

Now;

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

$\longrightarrow\tt{Surface\:Area\:of\:cube=6\times (8)^{2} }\\\\\longrightarrow\tt{Surface\:Area\:of\:cube=6\times 64}\\\\\longrightarrow\bf{Surface\:Area\:of\:cube=384\:sq.units}}$