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qwelly [4]
3 years ago
10

Please help find the central angle and perimeter !

Mathematics
1 answer:
sveticcg [70]3 years ago
3 0

Step-by-step explanation:

We will have the following

*First: We have that the area of a sector of a circle is given by the expression:

A = r²a/2

Here r is the radius and alpha is the central angle.

*Second: We determine the central angle as follows:

36\pi  =

(12)²a/2 ➡️ a = 36í•2/(12) ²➡️

a =  \frac{1}{2} \pi

So, the central angle has a measurement of 1/2 pi.

Third: We determine the perimeter of the sector as follows:

First: we determine the arc length with two times the radius, that is:

p = 2(12) +

6\pi

➡️ p = 24 +

6\pi

<em>So</em><em>,</em><em> </em><em>the</em><em> </em><em>perimeter</em><em> </em><em>of</em><em> </em><em>the</em><em> </em><em>sector</em><em> </em><em>is</em><em> </em><em>2</em><em>4</em><em>+</em><em> </em><em>6pi</em><em> </em><em>meters</em><em> </em><em>[</em><em> </em><em>Approximately</em><em> </em><em>4</em><em>3</em><em> </em><em>meters</em><em>]</em><em>.</em>

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The volume of the cone is:

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V = \frac{3900}{3}\pi

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