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butalik [34]
2 years ago
5

A sector with a radius of 8 cm has an area of 56pi cm2. What is the central angle measure of the sector in radians?

Mathematics
1 answer:
Maurinko [17]2 years ago
6 0

Answer:

\frac{7\pi}{4}.

Step-by-step explanation:

Given information:

Radius of circle = 8 cm

Area of sector = 56\pi\text{ cm}^2

Formula for area of sector is

A=\dfrac{1}{2}\theta r^2

where, r is radius and \theta is central angle in radian.

Substitute A=56\pi and r=8 in the above formula.

56\pi=\dfrac{1}{2}\theta (8)^2

56\pi=\dfrac{64}{2}\theta

56\pi=32\theta

\dfrac{56\pi}{32}=\theta

\dfrac{7\pi}{4}=\theta

Therefore, the measure of the sector in radians is \frac{7\pi}{4}.

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Step-by-step explanation:

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(1) Commutative property

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Step-by-step explanation:

We proceed to solve algebraically and explain each step:

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(4) Compatibility with multiplication/Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

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