Calculate the surface area

Here are the calculations for the surface area of the cone.

The dimensions of the cone are:

• Radius ($r$) = $3 \text{ cm}$
• Slant height ($l$) = $5 \text{ cm}$

Step 1: Calculate the surface area of the cone.
The formula for the total surface area of a cone is $SA = \pi r^2 + \pi r l$.

$$SA = \pi (3 \text{ cm})^2 + \pi (3 \text{ cm}) (5 \text{ cm})$$ $$SA = \pi (9 \text{ cm}^2) + \pi (15 \text{ cm}^2)$$ $$SA = 9 \pi \text{ cm}^2 + 15 \pi \text{ cm}^2$$ $$SA = 24 \pi \text{ cm}^2$$

Using $\pi \approx 3.14159$:

$$SA \approx 24 \times 3.14159 \text{ cm}^2$$ $$SA \approx 75.39816 \text{ cm}^2$$

Rounding to two decimal places:

$$SA \approx 75.40 \text{ cm}^2$$

The surface area of the cone is $\text{75.40 cm}^2*$.