Question

Find the surface area of a sphere of radius: 
(i) 10.5 cm 
(ii) 5.6 cm
(iii) 14 cm

Answer 1

We are given the radii of the spheres. The formula for the surface area \( A \) of a sphere is:

\[ A = 4 \pi r^2 \] where \( r \) is the radius of the sphere.

Step-by-Step Solution:

1. For radius = 10.5 cm:

Substituting \( r_1 = 10.5 \, \text{cm} \) into the surface area formula: \[ A_1 = 4 \pi (10.5)^2 = 4 \pi \times 110.25 = 441 \pi \, \text{cm}^2 \] Using \( \pi = 3.14 \): \[ A_1 = 441 \times 3.14 = 1388.94 \, \text{cm}^2 \]

2. For radius = 5.6 cm:

Substituting \( r_2 = 5.6 \, \text{cm} \) into the surface area formula: \[ A_2 = 4 \pi (5.6)^2 = 4 \pi \times 31.36 = 125.44 \pi \, \text{cm}^2 \] Using \( \pi = 3.14 \): \[ A_2 = 125.44 \times 3.14 = 393.30 \, \text{cm}^2 \]

3. For radius = 14 cm:

Substituting \( r_3 = 14 \, \text{cm} \) into the surface area formula: \[ A_3 = 4 \pi (14)^2 = 4 \pi \times 196 = 784 \pi \, \text{cm}^2 \] Using \( \pi = 3.14 \): \[ A_3 = 784 \times 3.14 = 2467.36 \, \text{cm}^2 \]

Final Answers:

• Surface area for radius 10.5 cm: \( A_1 = 1388.94 \, \text{cm}^2 \)
• Surface area for radius 5.6 cm: \( A_2 = 393.30 \, \text{cm}^2 \)
• Surface area for radius 14 cm: \( A_3 = 2467.36 \, \text{cm}^2 \)