Question

the surface area of this cone is 602.88 square meters. what is the slant height of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 8 m s ≈ □ meters submit

Explanation:

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

The surface area \( SA \) of a cone is given by the formula \( SA=\pi r^{2}+\pi r s \), where \( r \) is the radius of the base, \( s \) is the slant height. We know that \( SA = 602.88\) square meters, \( r = 8\) meters, and \( \pi\approx3.14 \). First, we calculate the area of the base \( \pi r^{2} \).
\[
\pi r^{2}=3.14\times8^{2}=3.14\times64 = 200.96
\]

Step2: Subtract the base area from the total surface area to get the lateral surface area

The lateral surface area \( LSA=\pi r s \) is equal to the total surface area minus the base area. So,
\[
LSA=SA - \pi r^{2}=602.88 - 200.96=401.92
\]

Step3: Solve for the slant height \( s \)

We know that \( LSA=\pi r s \), so we can solve for \( s \) by rearranging the formula: \( s=\frac{LSA}{\pi r} \). Substitute \( LSA = 401.92 \), \( \pi = 3.14 \), and \( r = 8 \) into the formula.
\[
s=\frac{401.92}{3.14\times8}=\frac{401.92}{25.12}=16.00
\]

Answer:

\( 16.00 \)