Question

Q6. If the surcase are of the cube is1536sqcm its volume is
cc."

Answer 1

• Volume of cube is 4096 cm³.

Step-by-step explanation:

Correct Question:-

• If the surface area of the cube is 1536 cm². It's Volume is :

_________________________________

Given:-

• Surface area of cube is 1536 cm².

To find:-

• Volume of cube.

Solution:-

• We need edge of cube for Volume of cube. So :

We know that,

$\boxed{\star \: \sf \bold{Total \: surface\:area \: of \: cube = 6 a^{2}}}$

In which,

• a is Edge or we can say side of cube.

Surface area = 1536

Put , surface area in formula :

$\longrightarrow \sf \bold{1536 = 6 {a}^{2} }$

$\longrightarrow \sf \bold{ \cfrac{1536}{6} = {a}^{2} }$

$\longrightarrow \sf \bold{256 = {a}^{2} }$

$\longrightarrow \sf \bold{ \sqrt{256} = a }$

$\longrightarrow \sf \bold{16 = a}$

Or, a = 16

Edge of cube is 16 cm.

$\boxed{\star \: \sf \bold{Volume \: of \: cube = a^{3}}}$

$\longrightarrow \sf \bold{ {(16)}^{3} }$

$\longrightarrow \sf \bold{16 \times 16 \times 16}$

$\longrightarrow \sf \bold{4096}$

Therefore,

Volume of cube is 4096 cm³.