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

Answer»

>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.


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