How do you find the surface area of a cone with base radius 3 cm and height 4 cm?

To find the surface area of a cone, use the formula: πr(r + l), where l is the slant height.

First, you need to determine the slant height (l) of the cone. The slant height can be found using the Pythagorean theorem, since the radius, height, and slant height form a right-angled triangle. The formula for the slant height is:

\[ l = \sqrt{r^2 + h^2} \]

Given the radius (r) is 3 cm and the height (h) is 4 cm, substitute these values into the formula:

\[ l = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm} \]

Now that we have the slant height, we can use the surface area formula for a cone. The surface area (A) of a cone is given by:

\[ A = \pi r (r + l) \]

Substitute the values of the radius (r = 3 cm) and the slant height (l = 5 cm) into the formula:

\[ A = \pi \times 3 \times (3 + 5) = \pi \times 3 \times 8 = 24\pi \text{ cm}^2 \]

So, the surface area of the cone is \( 24\pi \text{ cm}^2 \). If you need a numerical value, you can approximate π as 3.14:

\[ A \approx 24 \times 3.14 = 75.36 \text{ cm}^2 \]

Therefore, the surface area of the cone is approximately 75.36 square centimetres.