Question

What is the surface area of a cone to the nearest foot with a radius of 4 ft. and a slant height of 10 ft.?

Answer 1

To find the surface area of a cone, you need to use the formula:

\[
\text{Surface Area} = \pi r (r + l)
\]

where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.

Given:
- Radius \( r = 4 \) ft,
- Slant height \( l = 10 \) ft.

Now, substitute the values into the formula:

\[
\text{Surface Area} = \pi \times 4 \times (4 + 10)
\]

First calculate \( 4 + 10 = 14 \):

\[
\text{Surface Area} = \pi \times 4 \times 14
\]

Then calculate \( 4 \times 14 = 56 \):

\[
\text{Surface Area} = 56\pi
\]

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

\[
\text{Surface Area} \approx 56 \times 3.14 \approx 175.84 \text{ ft}^2
\]

Finally, rounding to the nearest foot:

\[
\text{Surface Area} \approx 176 \text{ ft}^2
\]

So, the surface area of the cone is approximately **176 ft²**.