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General

General

Easy

Question

The Volume of a cube is 512 cubic cm.After a smaller cube is out off from it its volume is 448 cubic cm.What is length of each side of the smaller cube ?

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 = $a cubed$ (where a = length of each edge of the cube.)

The correct answer is: Length of each side of the smaller cube is 4 cm.

Step-by-step solution:
From the given information, we get-
Volume of the original cube = 512 $c m cubed$ .
Volume of the resultant cube = 448 $c m cubed$ .
∴ Volume of small cube = Volume of the original cuboid - Volume of the resultant cube
∴ Volume of small cube = 512 - 448 ................................................................... (From given information)
∴ Volume of small cube = 64 $c m cubed$ ................................................................................. (Equation i)
We know that- Volume of the small cube = $open parentheses L e n g t h space o f space i t s space e d g e close parentheses cubed$ .
∴ 64 = $open parentheses L e n g t h space o f space i t s space e d g e close parentheses cubed$ ....................................................... (From Equation i)
∴ $cube root of 64$ = length of its edge .......................................................... (Taking cube root both the sides)
∴ 4 = length of its edge

∴ Length of each side of the smaller cube is 4 cm.

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