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A circle has a radius of 9 cm and a sector of the circle has an arc length of 9.7 cm.

The angle at the centre of the sector is X°.

Calculate the value of x to the nearest degree.

A circle has a radius of 9 cm and a sector of the circle has an arc length of 9.7 cm-example-1

2 Answers

5 votes

Answer:

62 DEGREES

Explanation:

User Stesch
by
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5 votes

Answer:

The value of X is 62 degrees

Explanation:

The arc length L of a circle is given by formula:

L= 2(pi)(r)X / 360 (1)

where pi = 3.14, r is the radius of the circle and X the angle that produces the arc. You want the angle X so we can simplify X in equation (1)

360L=2(pi)(r)X

360L/2(pi)(r)= X

X = 360L/2(pi)(r)

We replace the radius r=9cm the arc L = 9.7 cm and pi and obtain

X = 360* (9.7 cm)/ 2(3.14)*(9cm) = 3492/56.52 = 61.78

That rounded to nearest degree is 62 degrees.

User DannySlor
by
9.0k points
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