Question

Find the volume of a sphere whose radius is
(i) 7 cm 
(ii) 0.63 m

Answer 1

Step 1: Formula for the Volume of a Sphere

The volume \( V \) of a sphere is given by the formula: \[ V = \frac{4}{3} \pi r^3 \] where \( r \) is the radius of the sphere.

Step 2: (i) For a sphere with radius \( 7 \, \text{cm} \):

Using the formula: \[ V = \frac{4}{3} \pi (7)^3 \] First, calculate \( (7)^3 \): \[ (7)^3 = 343 \] Now, calculate the volume: \[ V = \frac{4}{3} \times 3.1416 \times 343 \approx 1436.76 \, \text{cm}^3 \] Therefore, the volume of the sphere is approximately \( 1436.76 \, \text{cm}^3 \).

Step 3: (ii) For a sphere with radius \( 0.63 \, \text{m} \):

Convert the radius to centimeters: \[ 0.63 \, \text{m} = 63 \, \text{cm} \] Now, using the formula: \[ V = \frac{4}{3} \pi (63)^3 \] First, calculate \( (63)^3 \): \[ (63)^3 = 250047 \] Now, calculate the volume: \[ V = \frac{4}{3} \times 3.1416 \times 250047 \approx 1047197.73 \, \text{cm}^3 \] Therefore, the volume of the sphere is approximately \( 1047197.73 \, \text{cm}^3 \).

Conclusion:

The volumes of the spheres are:

• (i) For the sphere with radius \( 7 \, \text{cm} \): \( 1436.76 \, \text{cm}^3 \)
• (ii) For the sphere with radius \( 0.63 \, \text{m} \): \( 1047197.73 \, \text{cm}^3 \)