Question

the surface area of a cube 36sq cm. whst is its volume?​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

$\Large{\underline{\bf{Given :}}}$

• Surface area of cube is 36 cm²

____________________________

$\Large{\underline{\bf{To \: Find :}}}$

Volume of cube

___________________________

$\Large{\underline{\bf{Solution :}}}$

We know that,

$\LARGE{\boxed{\boxed{\orange{\sf{Surface \: Area = 6a^2}}}}}$

(Putting Values)

36 = 6a²

36/6 = a²

√6 = a

$\large{\boxed{\boxed{\purple{\sf{Side = \sqrt{6}}}}}}$

$\rule{200}{2}$

Now,

$\LARGE{\boxed{\boxed{\green{\sf{Volume = a^3}}}}}$

Volume = (√6)³

Volume = √6 * √6 * √6

Volume = 6√6

$\large{\boxed{\boxed{\blue{\sf{Volume = 6 \sqrt{6}}}}}}$

$\rule{200}{2}$

#answerwithquality

#BAL

Answer 2

$\Huge{\boxed{\boxed{\mathsf{\purple{ANSWER \colon }}}}}$

Given,

The surface area of the cube is 36 cm².

Let a be the side of the cube

The Total Surface Area of a cube is given by :

$\huge{ \boxed{ \boxed{ \tt{ \green{6 {a}^{2} }}}}}$

Note

Surface area can mean both Total Surface Area and Lateral Surface Area of the Plane. Generally,it is assumed to be the TSA of the plane.

Implies,

$\large{ \sf{6 {a}^{2} = 36 }} \\ \\ \large{\implies \: \sf{ {a}^{2} = 6}} \\ \\ \huge{ \implies \: \boxed{ \boxed{ \sf{a = \sqrt{6} \: cm}}}} \:$

Volume of a cube is given by

$\huge{ \boxed{ \boxed{ \tt{ \green{{a}^{ 3} }}}}}$

$\large{ \longrightarrow \: \sf{v = {\sqrt{6} }^{3} }} \\ \\ \huge{ \longrightarrow \: \boxed{ \boxed{\sf{v = 6 \sqrt{6} \: {cm}^{3} }}}}$

Thus,the volume of the cube is 6√6 cm³

#BAL

#AnswerWithQuality