Question

question
find the surface area of the figure. round to the nearest hundredths when necessary.
(figure of a cone with height 14 in and radius 9 in)
answer attempt 2 out of 2

Explanation:

Step1: Recall the formula for the surface area of a cone

The surface area \( S \) of a cone is given by the formula \( S=\pi r(r + l) \), where \( r \) is the radius of the base and \( l \) is the slant height of the cone. From the diagram, we know that the radius \( r = 9 \) in and the slant height \( l=14 \) in.

Step2: Substitute the values into the formula

Substitute \( r = 9 \) and \( l = 14 \) into the formula \( S=\pi r(r + l) \).
First, calculate \( r + l=9 + 14=23 \).
Then, \( S=\pi\times9\times23 \).
Calculate \( 9\times23 = 207 \), so \( S = 207\pi \).
Using the approximation \( \pi\approx3.14159 \), we get \( S\approx207\times3.14159 \).
\( 207\times3.14159 = 207\times3+207\times0.14159=621+29.30913 = 650.30913 \).
Rounding to the nearest hundredth, we look at the thousandth place digit which is 9, so we round up the hundredth place. So \( S\approx650.31 \) square inches.

Answer:

\( 650.31 \) square inches