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alexdok [17]
3 years ago
10

What is the surface area of this right circular cone?

Mathematics
1 answer:
docker41 [41]3 years ago
3 0

Answer:

○ B) 624π mm.²

Step-by-step explanation:

\pi r(r +  \sqrt{ {r}^{2} +  {h}^{2}}) = S. A. \\  \\ \pi (12)(12 + \sqrt{{12}^{2} + {40}^{2}}) \\  \\ 12\pi(12 + \sqrt{1744}) = 12\pi(12 + 38) = 12\pi(50) = 600\pi \\  \\ 600\pi ≈ 624\pi

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For number 4, we'll need a few facts to answer our question:

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- The interior angles of a triangle add up to 180°

Given those, we notice that the one unlabeled angle in the figure shares a line with 156°. In fact, this angle is <em>supplementary</em> to 156°, which means that the two add up to 180°. To find the measure of this mystery angle, we can subtract 156 from 180 to obtain 180 - 156 = 24°.

Now, let's look at the triangle. We already know the measure of one of the angles is 24°, and the other two are x°. What else do we know about the angles of a triangle? From the two facts listed at the beginning, we know their interior angles add up to 180°, so let's use that fact to solve for x.

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Solving for x:

(2x+24)-24=180-24\\2x=156\\(2x)/2=(156)/2\\x=78

So, x = 78°.

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