Question

Find the surface area of a sphere of diameter:
(i) 14 cm
(ii) 21 cm
(iii) 3.5 m

Answer 1

We are given the diameters 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 diameter = 14 cm:

The radius \( r_1 = \frac{14}{2} = 7 \, \text{cm} \). Substituting into the surface area formula: \[ A_1 = 4 \pi (7)^2 = 4 \pi \times 49 = 196 \pi \, \text{cm}^2 \] Using \( \pi = 3.14 \): \[ A_1 = 196 \times 3.14 = 615.44 \, \text{cm}^2 \]

2. For diameter = 21 cm:

The radius \( r_2 = \frac{21}{2} = 10.5 \, \text{cm} \). Substituting into the surface area formula: \[ A_2 = 4 \pi (10.5)^2 = 4 \pi \times 110.25 = 441 \pi \, \text{cm}^2 \] Using \( \pi = 3.14 \): \[ A_2 = 441 \times 3.14 = 1388.94 \, \text{cm}^2 \]

3. For diameter = 3.5 m:

The radius \( r_3 = \frac{3.5}{2} = 1.75 \, \text{m} \). Substituting into the surface area formula: \[ A_3 = 4 \pi (1.75)^2 = 4 \pi \times 3.0625 = 12.25 \pi \, \text{m}^2 \] Using \( \pi = 3.14 \): \[ A_3 = 12.25 \times 3.14 = 38.465 \, \text{m}^2 \]

Final Answers:

• Surface area for diameter 14 cm: \( A_1 = 615.44 \, \text{cm}^2 \)
• Surface area for diameter 21 cm: \( A_2 = 1388.94 \, \text{cm}^2 \)
• Surface area for diameter 3.5 m: \( A_3 = 38.465 \, \text{m}^2 \)