Question

The edge of a cube is 20 cm. How many small cubes of 4 cm edge can be formed from this cube?
A.4
B.32
C.64
D.125

Answer 1

Hint: Volume of the cube is calculated using the formula, ${\text{side}} \times {\text{side}} \times {\text{side}}$.We will first find the volume of the cube with edge 20 cm. Then, find the volume of the cube with an edge 4 cm. Then, divide the volume of the cube with edge as 20 cm by volume of cube with edge as 4 cm to find the number of small cubes that can be formed.

Complete step-by-step answer:
Let us first calculate the volume of the cube with an edge as 20 cm.
The volume of the cube is calculated using the formula, ${\text{side}} \times {\text{side}} \times {\text{side}}$
Thus, the volume of the cube with edge as 20 cm is given by ${\text{20}} \times {\text{20}} \times {\text{20}}$
Now, calculate the volume of the cube with the length of the edge as 4 cm.
Thus, the volume of the cube with edge as 4 cm is calculated as ${\text{4}} \times 4 \times {\text{4}}$
To find the number of cubes of edge 4 cm that can be made using the cube of 20 cm, we will divide the volume of the cube with edge as 20 cm by volume of cube with edge as 4 cm.
Number of cubes that can be made are $\dfrac{{{\text{20}} \times {\text{20}} \times {\text{20}}}}{{{\text{4}} \times 4 \times {\text{4}}}} = 5 \times 5 \times 5 = 125$
Hence, option D is correct.

Note: Volume is the amount of space taken by an object. To find the number of cubes of edge 4 cm that can be made using the cube of 20 cm, we will divide the volume of the cube with edge as 20 cm by the volume of the cube with edge as 4 cm.