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Find the volume of a cube whose surface area is $150 m 2$ .

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121

m 3

m 3

m 3

125

m 3

answer is D.

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Detailed Solution

It is given a cube of surface area

150 m 2

.
We know the surface area of a cube of edge

a

6 a 2

.
Equate the formula of surface area with a given surface area.

⇒ 6 a 2 = 150

Dividing both sides by 6,

⇒ 6 a 2 6 = 1506

Cancel the same factors from both numerator and denominator.

⇒ a 2 = 25

… (1)
Take the square root on both sides of the equation.

⇒ a 2 = 25

⇒ a = 5 m

The formula of volume of the cube as

V = a 3

.
Substituting the value of

a = 5

in equation,

⇒ V = 53

⇒ V = 5 × 5 × 5

⇒ V = 125 m 3

Therefore, the volume of a cube having a surface area 150

m 2

is 125

m 3

.
Hence option (4) is correct.

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