Question

determine the surface area of a cone if the radius of the base is 8 in and the slant height is 10in. use pi and round answer to the nearest hundredth

Answer 1

To calculate the surface area of a cone, we can use the formula:

\[
\text{Surface Area} = \pi r^2 + \pi r l
\]

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

Given:
- \( r = 8 \) inches
- \( l = 10 \) inches

First, we calculate the area of the base:

\[
\text{Base Area} = \pi r^2 = \pi (8^2) = \pi (64) = 64\pi
\]

Next, we calculate the lateral surface area:

\[
\text{Lateral Surface Area} = \pi r l = \pi (8)(10) = 80\pi
\]

Now, we can combine these to find the total surface area:

\[
\text{Surface Area} = 64\pi + 80\pi = 144\pi
\]

Now, we’ll calculate \( 144\pi \) using \( \pi \approx 3.14 \):

\[
\text{Surface Area} \approx 144 \times 3.14 = 452.16
\]

Rounding to the nearest hundredth, the surface area of the cone is:

\[
\boxed{452.16} \, \text{square inches}
\]