Question

Find the curved surface area of a cylinder having a base radius of 4 cm and a height of 9 cm.

Answer 1

The formula for the curved surface area (lateral surface area) of a cylinder is given by:

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

where:
- \( r \) is the base radius,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately \( 3.14 \) or \( \frac{22}{7} \).

For the given cylinder:
- Base radius \( r = 4 \) cm,
- Height \( h = 9 \) cm.

Substituting these values into the formula:

\[
\text{Curved Surface Area} = 2 \pi (4) (9)
\]

Calculating this:

\[
\text{Curved Surface Area} = 2 \pi \cdot 36 = 72\pi
\]

Now, substituting \( \pi \approx 3.14\):

\[
\text{Curved Surface Area} \approx 72 \times 3.14 \approx 226.08 \text{ cm}^2
\]

Therefore, the curved surface area of the cylinder is:

\[
72\pi \text{ cm}^2 \quad \text{or} \quad \approx 226.08 \text{ cm}^2
\]