Question

If the length of the diagonal of a cube is 4√3 cm., Then let calculated the total surface of the cube.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{T.S.A\:of\:cube=96\:cm^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies Diagonal \: of \: cube = 4 \sqrt{3} \: cm \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies T.S.A \: of \: cube = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Diagonal \: of \: cube = \sqrt{3} a \\ \\ \tt: \implies 4 \sqrt{3} = \sqrt{3} a \\ \\ \tt: \implies a = \frac{4 \sqrt{3} }{ \sqrt{3} } \\ \\ \green{\tt: \implies a = 4 \: cm} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies T.S.A\: of \: cube = 6 {a}^{2} \\ \\ \tt: \implies T.S.A \: of \: cube =6 \times {4}^{2} \\ \\ \tt: \implies T.S.A \: of \: cube = 6 \times 16 \\ \\ \green{\tt: \implies T.S.A \: of \: cube =96 \: {cm}^{2} } \\ \\ \blue{ \bold{Some \: related \: formula}} \\ \orange{\tt \circ \: C.S.A\: of \: cube = 4 {a}^{2} } \\ \\ \orange{\tt \circ \: Volume \: of \: cube = {a}^{3} }$

Answer 2

Step-by-step explanation:

Given -

Length of the diagonal of a cube is 4√3 cm

To Find -

TSA of cube

Now,

As we know that :-

• Diagonal of a cube = √3a

here,

a = side

As Given -

• Diagonal of a cube is 4√3 cm

» 4√3 = √3a

» 4√3/√3 = a

• » a = 4 cm

Now,

As we know that :-

TSA of cube = 6a²

here,

a = side

» 6(4)²

» 6 × 16

» 96 cm²

Hence,

The TSA of cube is 96 cm²

Formula Used :-

• TSA of cube = 6a²
• Diagonal of a cube = √3a

Some related formulas :-

• Volume of cube = a³
• CSA of cube = 4a²