Question

the length of a diagonal of a cube is 7√3 cm.find the surface area​

Answer 1

$\huge{\mathfrak{\blue{\underline{\underline{\pink{SOLUTION:-}}}}}}$

Diagonal = 7√3

Also, Diagonal = √2 a

A.T.Q.

Diagonal = √2 a

7 √3 = √2 a

7√3 / √2 = a

Surface area = 6(a)²

=> 6 × ( 7√3 / √2)²

=> 6 × ( 147 / 2)

=> 3 × 147

=> 441cm²

Answer 2

$\LARGE\mathfrak{\pink{Solution:-}}$

$\large\mathbb{\orange{GIVEN:-}}$

• The length of a diagonal of a cube is $7\sqrt{3}$ cm.

$\large\mathbb{\purple{TO FIND:-}}$

The surface area.

$\large\mathbb{\green{FORMULA:-}}$

$Diagonal \: o f \: a \: cube (d)= \sqrt{3} a$

$Total \: Surface \: Area(T.S.A) = 6 {a}^{2}$

(Where d is diagnol and a is the side of the cube.)

$\large\mathbb{\red{ACCORDING \:TO\: THE\: QUESTION:-}}$

$d = \sqrt{3} a \\ \\ \implies \: 7 \sqrt{3} = \sqrt{3} a\\ \\ \implies \:a = \frac{ 7\sqrt{3} }{ \sqrt{3} } \\ \\ \implies \:a =7 \: cm$

Side = 7 cm.

$T.S.A = 6 {a}^{2} \\ \\ \implies \:T.S.A =6 \times {7}^{2} \\ \\ \implies \:T.S.A = 294 \: {cm}^{2}$

$\large\mathbb{\purple{ANSWER:-}}$

$\\ \implies \boxed{T.S.A = 294 \: {cm}^{2} }$