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Jlenok [28]
3 years ago
7

The cone shown has a diameter of 18 meters and a slant height of 15 meters. Which choice is closest to the lateral surface area?

Use 3.14 to approximate pi.
Mathematics
2 answers:
never [62]3 years ago
7 0
If you unfurl the lateral "face" of a cone, you get the sector of a circle whose central angle subtends an arc with length L equal to the circumference of the cone's base, and a radius equal to the slant height s of the cone.

Since the diameter of the base is 18m, the circumference of the base is about 3.14\times18=56.52 meters, so this is the value of L.

You're given a slant height of s=15 meters.

Now, the following proportional relation holds for any circle:

\dfrac{\text{area of sector}}{\text{area of circle}}=\dfrac{\text{arc length of sector}}{\text{circumference of circle}}

This translates to

\dfrac A{\pi\times s9^2}=\dfrac s{2\pi s\times9}

(remember, we're talking about a sector of a circle with radius s and arc length 18\pi). Solving for A:

\dfrac A{81\times3.14}=\dfrac{15}{18\times15\times3.14}
A=\dfrac92=4.5

So the area of the lateral face is approximately 4.5 square meters.
nadezda [96]3 years ago
4 0

Its 424 square meters


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