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inysia [295]
3 years ago
10

In a circle, a 90° sector has an area of 36π in2. What is the radius of this circle?

Mathematics
2 answers:
34kurt3 years ago
6 0

Answer:

r = 12 in

Step-by-step explanation:

A = \frac{1}{4} r^{2} \pi \\\\r = \sqrt{\frac{4A}{\pi } } = \sqrt{\frac{4 * 36\pi }{\pi } } = 2 * 6 = 12\ in

mamaluj [8]3 years ago
4 0

Answer:

r = 12 in

Step-by-step explanation:

recall that a full circle is represented by a sector that is 360°

in our case, the given sector is 90°

Hence our sector is 90° / 360° = 1/4 of a circle

It is also given that our 90° sector (which we now know is 1/4 of a circle) has an area of 36π in² and recall that the area of a full circle is πr²   (where r is the radius).

Hence,

πr² = 4 x area of 90° sector

πr² = 4 x 36π

πr² = 144π  (divide both sides by π)

r² = 144

r = √144

r = 12 in

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Step-by-step explanation:

You can calculate the surface area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are:  Three different rectangles and two equal triangles.

The formula for calculate the  area of a rectangle is:

A=lw

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The formula for calculate the  area of a triangle is:

A=\frac{bh}{2}

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You can observe that the hypotenuse of the each triangle is the width of one of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

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