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11111nata11111 [884]
2 years ago
8

What is the diameter of circle T?

Mathematics
1 answer:
Ratling [72]2 years ago
5 0

Answer:

Diameter = 16

Step-by-step explanation:

Given

\theta = 72

Sector = \frac{64}{5}\pi

Required

Calculate the diameter

The area of a sector is:

Area = \frac{\theta}{360} * \pi r^2

Substitute values for Area and \theta

\frac{64}{5}\pi = \frac{72}{360} * \pi r^2

Divide both sides by \pi

\frac{64}{5} = \frac{72}{360} * r^2

Make r^2 the subject

\frac{64*360}{5*72} = r^2

\frac{64*360}{360} = r^2

64 = r^2

Take positive square roots of both sides

\sqrt{64} = r

8 = r

r = 8

The diameter is then calculated as:

Diameter = 2r

Diameter = 2*8

Diameter = 16

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