Question

find the surface area of the figure. round to the nearest hundredths when necessary. 14 in 9 in

Explanation:

Step1: Calculate the slant height

Using the Pythagorean theorem \(l = \sqrt{h^{2}+r^{2}}\), where \(h = 14\) in and \(r=9\) in.
\(l=\sqrt{14^{2}+9^{2}}=\sqrt{196 + 81}=\sqrt{277}\approx16.64\) in.

Step2: Calculate the surface area of the cone

The formula for the surface area of a cone is \(S=\pi r(r + l)\).
Substitute \(r = 9\) in and \(l\approx16.64\) in.
\(S=\pi\times9\times(9 + 16.64)=9\pi\times25.64\)
\(S\approx9\times3.14\times25.64\)
\(S\approx28.26\times25.64\approx724.69\) in².

Answer:

\(724.69\) in².