Question

16.The length of the diagonal of a cube is 12√3 cm,then its surface area is : *

432 square cm

900 square cm

864 square cm

None of these

​

Answer 1

$\underline{\bf{Given:-}}$

✭Length of Diagonal = $\sf 12\sqrt{3}cm$

$\underline{\bf{Find:-}}$

✯Total Surface Area of Cube

$\underline{\bf{Solution:-}}$

we, know that

$\underline{\boxed{ \sf Length \: of \: Diagonal = \sqrt{3} \times side}}$

where,

• Length of Diagonal = $\sf 12\sqrt{3}cm$

So,

$\implies \sf Length \: of \: Diagonal = \sqrt{3} \times side$

$\implies \sf 12 \sqrt{3} = \sqrt{3} \times side$

$\implies \sf \dfrac{ 12 \sqrt{3} }{ \sqrt{3} } =side$

$\implies \sf 12cm =side$

$\small{\therefore \sf Side = 12cm}$

Now, using

$\underline{\boxed{ \sf Total \: Surface \: Area= 6 {a}^{2} }}$

where,

• Side, a = 12cm

So,

$\dashrightarrow\sf Total \: Surface \: Area= 6 {a}^{2}$

$\dashrightarrow\sf Total \: Surface \: Area= 6 {(12)}^{2}$

$\dashrightarrow\sf Total \: Surface \: Area= 6 \times 144$

$\dashrightarrow\sf Total \: Surface \: Area= 864 {cm}^{2}$

$\small{\therefore\sf Total \: Surface \: Area= 864 {cm}^{2}}$

Hence, Correct Option is (C) 864cm²