Question

what is the surface area of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 17 m 8 m square meters submit

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 diagram, the radius \( r = 8\) m and the slant height \( l=17\) m.

Step3: Substitute the values into the formula

Substitute \( r = 8\), \( l = 17\) and \( \pi\approx3.14\) into the formula:
\( S=3.14\times8\times(8 + 17) \)
First, calculate the sum inside the parentheses: \( 8+17 = 25\)
Then, multiply: \( 3.14\times8\times25=3.14\times(8\times25)=3.14\times200 = 628.00\) (Wait, no, wait. Wait, the formula is \( \pi r^2+\pi rl\), which is the same as \( \pi r(r + l)\). Wait, let's recalculate. Wait, \( r = 8\), \( l=17\). So \( \pi r^2+\pi rl=\pi r(r + l)\). So \( 3.14\times8\times(8 + 17)=3.14\times8\times25\). Wait, \( 8\times25 = 200\), \( 3.14\times200=628\)? Wait, no, that can't be right. Wait, no, wait, the lateral surface area is \( \pi rl\) and the base area is \( \pi r^2\). So let's calculate lateral surface area: \( \pi rl=3.14\times8\times17\). Let's calculate that: \( 3.14\times8 = 25.12\), \( 25.12\times17 = 427.04\). Then the base area: \( \pi r^2=3.14\times8^2=3.14\times64 = 200.96\). Then total surface area is \( 427.04+200.96=628.00\). Wait, that's the same as before. So the surface area is 628.00 square meters? Wait, but let's check again. The formula for the surface area of a cone is \( S=\pi r^2+\pi rl=\pi r(r + l) \). So \( r = 8\), \( l = 17\). So \( 3.14\times8\times(8 + 17)=3.14\times8\times25\). \( 8\times25 = 200\), \( 3.14\times200 = 628.00\). So that's correct.

Answer:

\( 628.00 \)