Question

the volume of a cube is 2197cu.m find the length of the side of the cube

Answer 1

Find the length of the side:

Formula : Volume = Length x Length x Length

Volume = Length³

Given that the length is 2197 m³

Length³ = 2197

Length = ∛2197

Length = 13 m

Answer: The length is 13m

Answer 2

$\underline{\mathfrak{Solution : }}$

$\text{We know that : }$

$\mathsf{\implies Volume \: of \: a \: Cube \: = \: (Side)^{3} }$

$\mathsf{\implies 2,197\:{m}^{3} \: = \: (Side)^{3}}$

$\mathsf{ \implies 13 \: \times \: 13 \: \times \: 13 \: {m}^{3} \: = \: (Side)^{3}}$

$\mathsf{\implies {(13\: m)}^{3} \: = \: {(Side)}^{3}}$

$\mathsf{\implies 13 \: m = \: {({(Side)}^{3})}^{\frac{1}{3}}}$

$\text{Using algebraic identity,}$

$\boxed{\mathsf{\implies {({a}^{m})}^{n} \: = \: {a}^{mn} }}$

$\mathsf{\implies 13 \: m =\: {(Side)}^{\cancel{3} \: \times \: \frac{1}{\cancel{3}}}}$

$\mathsf{\therefore \quad Side \: = \: 13 \: m }$

$\boxed{\underline{\mathfrak{Hope \: \: it \: \: helps \: \: !!}}}$