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General

General

Easy

Question

Find the volume of a cube whose surface area is 150 $c m squared$

hint Hint:

A cube is a solid 3 dimensional figure with six-faces, 8 vertices and 12 edges. Its faces are squares.

Volume is the capacity of a certain object to carry or hold another objects within i.e. the amount of space that the object holds. Volume of a cube = $a cubed$ .

Surface area of an object refers to the area of all the surfaces of an object. Surface Area of a cube = $6 a squared$ ., where a = length of each edge of the cube.

The correct answer is: Volume of the given cube is 125 cm3.

Step-by-step solution:
From the given information, we observe that-
Surface area of the given cube = 150 $c m squared$ …...................................................... (Equation i)
Now, we know that-
Surface area of a cube = $6 a squared$
∴ Surface area of the given cube = $6 a squared$
∴ 150 = $6 a squared$ .............................................................. (From Equation i)
∴ 25 = $a squared$ ..................................................................... (Dividing both the sides by 6)
∴ 5 = a ........... (Taking square root both the sides) ........................... (Equation ii)
Now, we know that-
Volume of a cube = $a cubed$
∴ Volume of the given cube = $a cubed$
∴ Volume of the given cube = $5 cubed$ ................................................................................................. (From Equation ii)
∴ Volume of the given cube = 125 $c m cubed$ .

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