Find the volume of a cube if each face of a cube has a perimeter of 32 cm -A- 343 cm 3- 512 cm 3C- 125 cm 3D- 216 cm 3

The correct option is B 512 cm^3 Let ABCD be a face of the cube whose side is a. Since nbsp;ABCD nbsp; is a square, Perimeter = 4a = 32 cm ⇒ a=32/4 nbs ...

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Standard VIII

Mathematics

Volume of a Cube

Find the volu...

Question

Find the volume of a cube if each face of a cube has a perimeter of $32 c m ?$

$343 c m^{3}$

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$512 c m^{3}$

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$216 c m^{3}$

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$125 c m^{3}$

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Solution

The correct option is B
$512 c m^{3}$

Let $A B C D$ be a face of the cube whose side is $a$ .

Since $A B C D$ is a square,

Perimeter $= 4 a = 32 c m$

$\Rightarrow a = \frac{32}{4} = 8 c m$

Hence, volume of cube $= a^{3} = 8^{3} = 512 c m^{3}$

Suggest Corrections

Find the volume of a cube if each face of a cube has a perimeter of 32 cm?

The correct option is B 512 cm3 Let ABCD be a face of the cube whose side is a. Since ABCD is a square, Perimeter =4a=32 cm ⇒a=324=8 cm Hence, volume of cube =a3=83=512 cm3

Find the volume of a cube if each face of a cube has a perimeter of $32 c m ?$

The correct option is B
$512 c m^{3}$

Let $A B C D$ be a face of the cube whose side is $a$ .

Since $A B C D$ is a square,

Perimeter $= 4 a = 32 c m$

$\Rightarrow a = \frac{32}{4} = 8 c m$

Hence, volume of cube $= a^{3} = 8^{3} = 512 c m^{3}$