Question

Find the volume of a cube whose surface area is 216m2. is the numerical value of the surface area same as that of its volume?.





please give me the answer in method​

Answer 1

Answer:

$\sf{\pink{Volume\:of\:cube\:=\:216\:m^{3}}}$

ExplanaTion:

It is given that surface area of a cube is 216 m²

We've to find the volume of cube.

We know that -

$\large{\boxed{\sf{\red{Surface\:area\:of\:cube\:=\:6a^{2}}}}}$

$\therefore$ 6a² = 216

$\longrightarrow$ a² = $\dfrac{216}{6}$

$\longrightarrow$ a² = 36

$\longrightarrow$ a = ±√36

Rejecting the negative value, we get,

$\longrightarrow$ $\sf{\blue{a = 6\:m}}$

We also know that,

$\large{\boxed{\sf{\green{Volume\:of\:cube\:=\:a^{3}}}}}$

$\longrightarrow$ Volume of cube = 6³

$\longrightarrow$ $\sf{\pink{Volume\:of\:cube\:=\:216\:m^{3}}}$

Yes, numerically value of surface area and volume is same.

Answer 2

GIVEN :

• Total surface area of cube = 216 cm².

TO FIND :

• The volume of the Cube.

SOLUTION :

$:\implies\sf 6\:(Edge)^{2}= TSA\:of\:cube\\\\\\:\implies\sf 6\:(Edge)^{2} = 216\:cm^{2}\\\\\\:\implies\sf (Edge)^{2} = \dfrac{216}{6}\\\\\\:\implies\sf (Edge)^{2} = 36 \\\\\\:\implies\sf Edge= \sqrt{36}\\\\\\:\implies\:\:\underline{\boxed{\sf Edge = 6\:cm}}$

Volume of the given cube = (Edge)³ = (6)³ = 216 cm³

$\therefore\:\underline{\textsf{ The Volume of the cube is \textbf{216 }} \sf cm^3}$

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