Question

Find the amount of water displaced by a solid spherical ball of diameter.
(i) 28 cm 
(ii) 0.21 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 ball with diameter 28 cm:

The radius \( r \) is half of the diameter: \[ r = \frac{28}{2} = 14 \, \text{cm} \] Now, calculate the volume of the sphere: \[ V = \frac{4}{3} \pi (14)^3 \] First, calculate \( (14)^3 \): \[ (14)^3 = 2744 \] Now, calculate the volume: \[ V = \frac{4}{3} \times 3.1416 \times 2744 \approx 11494.04 \, \text{cm}^3 \] Therefore, the amount of water displaced by the ball is approximately \( 11494.04 \, \text{cm}^3 \).

Step 3: (ii) For a ball with diameter 0.21 m:

Convert the diameter to centimeters: \[ 0.21 \, \text{m} = 21 \, \text{cm} \] The radius \( r \) is half of the diameter: \[ r = \frac{21}{2} = 10.5 \, \text{cm} \] Now, calculate the volume of the sphere: \[ V = \frac{4}{3} \pi (10.5)^3 \] First, calculate \( (10.5)^3 \): \[ (10.5)^3 = 1157.625 \] Now, calculate the volume: \[ V = \frac{4}{3} \times 3.1416 \times 1157.625 \approx 4841.64 \, \text{cm}^3 \] Therefore, the amount of water displaced by the ball is approximately \( 4841.64 \, \text{cm}^3 \).

Conclusion:

The amount of water displaced by the spherical balls are:

• (i) For the ball with diameter 28 cm: \( 11494.04 \, \text{cm}^3 \)
• (ii) For the ball with diameter 0.21 m (21 cm): \( 4841.64 \, \text{cm}^3 \)