Question

A cone has a base radius of 9 ft. and a slant height of 16 ft. Which of the following correctly calculates the surface area of the cone? Use π≈3.14 .

Answer 1

To calculate the surface area of a cone, you need to find the sum of the lateral surface area and the area of the base.

The formulas for the surface area are:

1. **Lateral Surface Area (LSA)**:
\[
\text{LSA} = \pi r l
\]
where \( r \) is the radius of the base and \( l \) is the slant height.

2. **Area of the Base (A)**:
\[
A = \pi r^2
\]

The total surface area \( SA \) of the cone is then:
\[
\text{SA} = \text{LSA} + A
\]

Given:
- \( r = 9 \, \text{ft} \)
- \( l = 16 \, \text{ft} \)

Now, calculate the lateral surface area (LSA):
\[
\text{LSA} = \pi \times r \times l = 3.14 \times 9 \times 16
\]

Calculating that:
\[
\text{LSA} = 3.14 \times 9 = 28.26
\]
Then multiply by 16:
\[
\text{LSA} = 28.26 \times 16 = 452.16 \, \text{ft}^2
\]

Next, calculate the area of the base:
\[
A = \pi r^2 = 3.14 \times 9^2 = 3.14 \times 81
\]

Calculating that:
\[
A = 3.14 \times 81 = 254.34 \, \text{ft}^2
\]

Finally, add the lateral surface area and the area of the base to get the total surface area:
\[
\text{SA} = \text{LSA} + A = 452.16 + 254.34 = 706.50 \, \text{ft}^2
\]

Thus, the surface area of the cone is **706.50 ft²**.