Question

what is the surface area of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 93 m 27 m

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.

Step2: Identify the values of \( r \) and \( l \)

From the problem, we have \( r = 27\space m \) (the radius of the base) and \( l=93\space m \) (the slant height of the cone). We are also given that \( \pi\approx3.14 \).

Step3: Substitute the values into the formula

Substitute \( r = 27 \), \( l = 93 \) and \( \pi=3.14 \) into the formula \( S=\pi r(r + l) \):
\[

$$\begin{align*} S&=3.14\times27\times(27 + 93)\\ &=3.14\times27\times120 \end{align*}$$

\]

Step4: Perform the multiplication

First, calculate \( 27\times120 = 3240 \). Then, multiply this result by \( 3.14 \):
\[
S=3.14\times3240
\]
\[
S = 10173.6
\]

Answer:

\( 10173.60 \) (rounded to the nearest hundredth)