Question

The total surface area of a cube is 1350sq.m. Find its volume ​

Answer 1

$\large \underline{\underline{\textsf{Answer}}}$

$\large \underline{\boxed{ \mathtt{Volume(V)\: of \: cube \: = 3375{m}^{3}}}}$

$\large \underline{\underline{\textsf{Step-by-step Explanation}}}$

Given

• The Total Surface area of Cube = 1350sq m

To Find

• Volume Of the cube

Solution

According to question

We know that the TSA of the Cube is 1350 m square

But we know that

$\boxed{\boxed{\bigstar \; \mathtt{TSA \:Of \: Cube = 6 \times {(Length)}^{2}}}}$

Where here

TSA = 1350 m. sq

Thus we have,

$\mathtt{\longrightarrow \: 6 \times {(Length)}^{2} = 1350m^2}$

$\mathtt{\longrightarrow \: {(Length)}^{2} = \dfrac{1350m^2}{6}}$

$\mathtt{\longrightarrow \: {(Length)}^{2} = 225{m}^{2}}$

$\mathtt{\longrightarrow \: Length = \sqrt{225{m}^{2}}}$

Therefore we have,

$\mathtt{\longrightarrow \: Length \: of \: cube \:= 15m}$

Now we know that,

$\boxed{\boxed{\bigstar \; \mathtt{Volume(V)\: of \: cube \: = {(Length)}^{3}}}}$

Now putting Value Of Length = 15m in the above formula we have,

$\mathtt{\longrightarrow \: Volume \: = {(15m)}^{3}}$

$\mathtt{\longrightarrow \: Volume \: = 3375{m}^{3}}$

Therefore We Have Required Answer =

$\boxed{ \mathtt{Volume(V)\: of \: cube \: = 3375{m}^{3}}}$

Answer 2

$\large \sf \underline{ \underline{ \:Given :</p><p> \: \: \: }}$

TSA of cube = 1350 m²

$\large \sf \underline{ \underline{ \:To \: find :</p><p> \: \: \: }}$

Volume of cube

$\large \sf \underline{ \underline{ \: Solution :</p><p> \: \: \: }}$

We know that ,

$\sf \large \fbox{ \fbox{TSA \: of \: cube = 6 \times {(side)}^{2} }}$

$\implies \sf 1350 = 6 \times {(side)}^{2} \\ \\ \implies \sf {(side)}^{2} = \frac{ \cancel{1350}}{ \cancel{6}} \\ \\ \implies \sf {(side)}^{2} = 225 \\ \\ \implies \sf side = \sqrt{225} \\ \\ \implies \sf side = 15 \: \:m$

Now , the volume of cube is given by

$\sf \large \fbox{ \fbox{ Volume \: of \: cube = {(side)}^{3} }}$

$\sf = {(15)}^{3} \\ \\ \sf = 3375 \: \: {m}^{2}$

Therefore , the volume of cube is 3375 m³