Question

The total surface area of a cube is 5400 cm². Find find the surface area of the vertical faces of the cube.

Answer 1

$\huge\bold{\mathtt{\purple{A{\pink{N{\green{S{\blue{W{\red{E{\orange{R}}}}}}}}}}}}}$$\huge \Rightarrow$

$\Large \bold\red {Solution:}$

Here, the total surface area = 5400 cm²,

Here, the total surface area = 5400 cm²,the surface area of the vertical faces = ?

The total surface area of a cube = $6l²$ ... (Formula)

$\Rightarrow$ $5400=6l²$

$\Rightarrow$ $l²= \frac {5400}{6}$ ...(1)

The surface area of the vertical faces of a cube = $4l²\:\:\:\:\:\:\:\:\:\:\:\:.$ ...(Formula)

$\Rightarrow$ $4l²=4× \frac {5400}{6}$

= 3600 cm²

$\large\bold\purple{Ans:}\Rightarrow$

The surface area of the vertical face of a cube is 3600 cm².

Answer 2

${\huge{\star{\underbrace{\tt{\red{Answer}}}}}}{\huge{\star}}$

$\Large{\blue{\tt{\underline{\underline{Given \ :-}}}}}$

• Total surface area of cube = 5400 cm²

$\Large{\green{\tt{\underline{\underline{To \ find \ :-}}}}}$

• Area of vertical face of cube

$\Large{\orange{\tt{\underline{\underline{Solution \ :-}}}}}$

${\boxed{\purple{\sf \star \ TSA \ of \ cube \ = \ 6 {a}^{2} }}}$

here ,

• a is the side of cube

Now

${\sf{\hookrightarrow \ 5400 \ = \ 6{a}^{2}}}$

${\sf{\hookrightarrow \ \frac{ \cancel{5400}}{ \cancel6} \ = \ {a}^{2}}}$

${\sf{\hookrightarrow \ {a}^{2} \ = \ 900}}$

${\sf{\hookrightarrow \ a \ = \ \sqrt{900} }}$

${\sf{\hookrightarrow \ a \ = \ 30cm}}$

___________________

${\sf{ Area \ of \ vertical \ faces \ = \ 4{a}^{2}}}$

${\bold{\leadsto \sf \ Area \ of \ vertical \ faces \ = \ 4 \times {30}^{2} }}$

${\sf{\leadsto \ Area \ of \ vertical \ faces \ = \ 4\times 900}}$

${\bf{\leadsto \ Area \ of \ vertical \ faces \ = \ 3600 {cm}^{2}}}$

Hence the area of the vertical faces of cube is 3600cm²

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