Question

The surface area of a cube is 1176 sq. cm. What is its volume?

Answer 1

Answer:

Given :-

• The surface area of a cube is 1176 cm².

To Find :-

• What is the volume of cube.

Formula Used :-

$\clubsuit$ Total Surface Area Of Cube Formula :

$\mapsto \sf\boxed{\bold{\pink{T.S.A_{(Cube)} =\: 6a^2}}}$

$\clubsuit$ Volume Of Cube Formula :

$\mapsto \sf\boxed{\bold{\pink{Volume_{(Cube)} =\: a^3}}}$

where,

• a = Side

Solution :-

First, we have to find the side :

Given :

• Surface Area of Cube = 1176 cm²

According to the question by using the formula we get,

$\implies \sf 6a^2 =\: 1176$

$\implies \sf a^2 = \dfrac{\cancel{1176}}{\cancel{6}}$

$\implies \sf a^2 =\: 196$

$\implies \sf a =\: \sqrt{196}$

$\implies \sf a =\: \sqrt{14 \times 14}$

$\implies \sf\bold{\purple{a =\: 14\: cm}}$

Now, we have to find the volume of cube :

Given :

• Side = 14 cm

According to the question by using the formula we get,

$\longrightarrow \sf Volume_{(Cube)} =\: a^3$

$\longrightarrow \sf Volume_{(Cube)} =\: (14)^3$

$\longrightarrow \sf Volume_{(Cube)} =\: 14 \times 14 \times 14$

$\longrightarrow \sf\bold{\red{Volume_{(Cube)} = 2744\: cm^3}}$

${\small{\bold{\underline{\therefore\: The\: volume\: of\: cube\: is\: 2744\: cm^3\: .}}}}$

Answer 2

${\large{\bf{\red{\clubs{\underline{Given :}}}}}}$

The surface area of a cube is 1176 sq. cm.

￣￣￣￣￣￣￣￣￣￣￣￣

${\large{\bf{\blue{\clubs{\underline{To Find :}}}}}}$

What is the volume of the cube.

￣￣￣￣￣￣￣￣￣￣￣￣

${\large{\bf{\orange{\clubs{\underline{Solution :}}}}}}$

Surface area of cube :

${\blue{\bigstar{\pink{\boxed{\mathfrak{= 6 {a}^{2} }}}}}}$

Here,

A = side

${\sf{\green{Surface \: area \: of \: cube = 6 {a}^{2} }}}$

${\sf{\green{1176 = 6 \times {a}^{2} }}}$

${\sf{\green{ \frac{1176}{6} = {a}^{2} }}}$

${\sf{\green { = {\cancel \frac{1176}{6} = {a}^{2} }}}}$

${\sf{\green{ \sqrt{196} = a }}}$

${\sf{\red{a = 14}}}$

Than,

Volume of cube :

${\blue{\bigstar{\pink{\boxed{\mathfrak{ = {side}^{3} }}}}}}$

${\sf{\green{Volume \: of \: cube = {side}^{3} }}}$

${\sf{\green{Side = a = 14}}}$

${\sf{\green{= {14}^{3} }}}$

${\blue{\underbrace{\red{\boxed{\bf{= 2,744 {cm}^{3} }}}}}}$

So,

${\tt{\green{Volume \: of \: given \: cube \: is \: 2744 {cm}^{3} .}}}$

￣￣￣￣￣￣￣￣￣￣￣￣

${\bf{\underline{\fcolorbox{green}{red}{\blue{ItzNobita5}}}}}$