Question

the surface area of a cube is 1176 cm². Find its volume​

Answer 1

TSA of cube = 6a² = 1176cm²

$\sf \orange{{a}^{2} = \cancel\dfrac{1176}{6} = 196}$

$\sf \green{{a}^{2} = 14 \: cm}$

Volume of cube = a²

$\sf \implies \red {(14 {)}^{3}}$

$\sf \implies \purple{2744 \: {cm}^{2}}$

Answer 2

$\LARGE \underline {\frak{ ~~~~~~~~~ \pink{Required \:Answer} ~~~~~~~~~}}$

We know:

$\bigstar \boxed{ \rm{}Volume~of~cube=(side)^3}$

Here as we can see to find volume we should know value of side

So first let's find side of cube

We know:

$\bigstar \boxed{ \rm{}Area~of~cube=6\times side^2}$

By using this formula we can find value of side of cube

$\dashrightarrow\sf{}Area~of~cube=6\times side^2$

$\dashrightarrow\sf{}1176=6\times side^2$

$\dashrightarrow\sf{} \dfrac{1176}{6} =side^2$

$\dashrightarrow\sf{} \cancel\dfrac{1176}{6} =side^2$

$\dashrightarrow\sf{} 196=side^2$

$\dashrightarrow\sf{}side^2 = 196$

$\dashrightarrow\sf{}side = \sqrt{196}$

$\dashrightarrow\sf{}side = {(196)}^{ \frac{1}{2} }$

$\dashrightarrow\sf{}side = {( {7}^{2} \times {2}^{2} )}^{ \frac{1}{2} }$

$\dashrightarrow\sf{}side = {( {7}\times {2} )}^{ \frac{2}{2} }$

$\dashrightarrow\sf{}side = {( {7}\times {2} )}^{ \cancel\frac{2}{2} }$

$\dashrightarrow\sf{}side = 7 \times 2$

$\dashrightarrow \underline{ \boxed{\sf{}side = 14 \: cm}}$

Now Let's find volume by using formula mentioned above

$\dashrightarrow \sf{}Volume~of~cube=(side)^3$

$\dashrightarrow \sf{}Volume~of~cube=(14)^3$

$\dashrightarrow \sf{}Volume~of~cube=14 \times 14 \times 14$

$\dashrightarrow \underline{ \boxed{ \sf{}Volume~of~cube=2744 {cm}^{3} }}$

$\therefore \underline{ \sf{}Volume~of~cube=2744 \: {cm}^{3} }$