Question

The diameter of a sphere is 14 cm. Calculate its curved surface area.

Answer 1

To calculate the curved surface area (also known as the lateral surface area) of a sphere, we can use the formula:

\[
\text{Curved Surface Area} = 4\pi r^2
\]

where \( r \) is the radius of the sphere.

First, we need to find the radius. Since the diameter of the sphere is 14 cm, the radius \( r \) is half of the diameter:

\[
r = \frac{\text{diameter}}{2} = \frac{14 \, \text{cm}}{2} = 7 \, \text{cm}
\]

Now, substituting the radius into the formula for the curved surface area:

\[
\text{Curved Surface Area} = 4\pi (7 \, \text{cm})^2
\]

Calculating \( (7 \, \text{cm})^2 \):

\[
(7 \, \text{cm})^2 = 49 \, \text{cm}^2
\]

Now substituting back into the area formula:

\[
\text{Curved Surface Area} = 4\pi \times 49 \, \text{cm}^2 = 196\pi \, \text{cm}^2
\]

If we want a numerical approximation, we can use \( \pi \approx 3.14 \):

\[
\text{Curved Surface Area} \approx 196 \times 3.14 \approx 615.44 \, \text{cm}^2
\]

Thus, the curved surface area of the sphere is:

\[
\text{Curved Surface Area} = 196\pi \, \text{cm}^2 \quad \text{or approximately} \, 615.44 \, \text{cm}^2
\]