Eli is making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use 3.14 for pi.(1 point)

Question

square inches.

Answer 1

To find the surface area of the cone peak, we need to calculate the lateral surface area and the base surface area. However, since we are talking about the roof peak and it does not have a base, we will only calculate the lateral surface area.

The formula for the lateral surface area \( A \) of a cone is given by:

\[ A = \pi r l \]

where:

• \( r \) is the radius of the base,
• \( l \) is the slant height.

First, we need to find the radius of the cone. The diameter of the cone is given as 14 inches, so the radius \( r \) is:

\[ r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ inches} \]

The slant height \( l \) is given as 20 inches.

Now we can substitute the values into the lateral surface area formula:

\[ A = \pi r l = 3.14 \times 7 \times 20 \]

Calculating this step-by-step:

1. Calculate \( r \times l \): \[ 7 \times 20 = 140 \]

2. Now multiply by \( \pi \): \[ A = 3.14 \times 140 = 439.6 \]

Thus, the lateral surface area of the cone peak is:

\[ \boxed{439.60} \text{ square inches} \]

Therefore, the surface area of the cone peak, rounded to the nearest hundredth, is 439.60 square inches.