Question

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
A. π : 2
B. π : 3
C. π : 4
D. π : 6

Answer 1

Answer:

Step-by-step explanation:

6

Answer 2

The ratio of the volume of the sphere to the volume of the cube is option (D), π : 6 .

• Let each side of the cube be x units.

Volume of a cube = (side)³

Therefore, volume of the given cube = x³ cubic units

• Since the sphere is inscribed in the cube, the diameter of the sphere will be equal to the length of  the side of the cube.

=> Diameter of the sphere = x units

=> Radius of the sphere = x / 2 units

• Now, volume of a sphere

= (4 / 3).π.(radius)³

Therefore, volume of the sphere = (4 / 3).π.(x / 2)³ cubic units

= (4 / 3).π.(x³ / 8) cubic units

= πx³ / ( 3 × 2) cubic units

= πx³ / 6 cubic units

• Now, ratio of the volume of the sphere to the volume of the cube = Volume of the sphere / Volume of the cube

=> Ratio =  (πx³ / 6) cubic units

/ (x³) cubic units

Or, ratio = πx³ / 6x³

Or, ratio = π / 6

Or, ratio = π : 6