Question: find the are of a cone r=4 h=5
1. **State the problem:** Find the surface area of a cone with radius $r=4$ and height $h=5$.
2. **Formula:** The total surface area $A$ of a cone is given by:
$$A = \pi r^2 + \pi r l$$
where $l$ is the slant height.
3. **Calculate the slant height $l$:**
Use the Pythagorean theorem:
$$l = \sqrt{r^2 + h^2} = \sqrt{4^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41}$$
4. **Calculate the surface area:**
$$A = \pi (4)^2 + \pi (4) \sqrt{41} = 16\pi + 4\pi \sqrt{41}$$
5. **Final answer:**
The surface area of the cone is:
$$A = 16\pi + 4\pi \sqrt{41}$$
which is approximately:
$$A \approx 16 \times 3.1416 + 4 \times 3.1416 \times 6.4031 = 50.265 + 80.425 = 130.69$$
So, the surface area is approximately $130.69$ square units.