Question

The surface area of a cube is 216m2 what is the volume of the cube

Answer 1

Given:-

• Total Surface Area of Cube is 216 m²

To Find:-

• Volume of Cube = ??

Solution:-

Let , The side of a Cube be a .

$\\\diamond{\underline{\underline{\sf {\;\; Calculating\; Side\; of \; Cube :-}}}}$

$\\ \pink \star \: \: {\underline{\boxed {\bf{ TSA_{ \red{ \{Cube \}}} \: = 6 {(a)}^{2} }}} }\; \red\bigstar$

Where,

• » TSA denotes Total Surface Area
• » a denotes Side of cube

$\\ \: \sf\implies \: TSA_{ \red{ \{Cube \}}} \: = 6 \: {(a)} \: ^{2}$

$\\ \: \sf\implies \: 216 \: = 6 \: {(a)} \: ^{2}$

$\\ \: \sf\implies \: {(a)} \: ^{2} \: = \: \frac{216}{6} \:$

$\\ \: \sf\implies \: {(a)} \: ^{2} \: = \: 36 \:$

$\\ \: \sf\implies \: a \: = \: \sqrt{ \: 36 \: } \: \:$

$\\ \: \sf\implies \: a \: = \: 6 \: {m}^{2} \: \:$

$\\ \implies{\underline{\boxed{\frak { Side = 6 \: m^3 }}}} \; \purple\bigstar$

$\qquad \rule{120pt}{3pt}$

$\\\diamond{\underline{\underline{\sf {\;\; Calculating\; Volume\; of \; Cube :-}}}}$

$\\ \pink \star \: \: {\underline{\boxed {\bf{ Volume_{ \red{ \{Cube \}}} \: = {(a)}^{3} }}} }\; \red\bigstar$

Where,

• » a denotes Side of cube

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

$\\ \: \sf\implies \: Volume_{ \red{ \{Cube \}}} \: = \: {(6)} \: ^{3}$

$\\ \: \sf\implies \: Volume_{ \red{ \{Cube \}}} \: = \: 216 \: {cm} \: ^{3}$

$\\ \implies{\underline{\boxed{\frak { Volume_{ \red{ \{Cube \}}} \: = \: 216 \: {cm} \: ^{3} }}}} \; \purple\bigstar$

$\\\qquad \rule{120pt}{3pt}$

Therefore, The Volume of Cube is 216 cm ³

Answer 2

Answer:

216 is correct answer. Please Mark it as brainlist answer.