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*Find the radius r of the circle if an arc of length 15 m on the circle subtends

ID: 2919753 • Letter: #

Question

*Find the radius r of the circle if an arc of length 15 m on the circle subtends a central angle of 5/6 rad. (Round your answer to two decimal places.)

r = 1 m

* This exercise involves the formula for the area of a circular sector.

Find the radius r of each circle if the area of the sector is 22.

r =

r =

*This exercise involves the formula for the area of a circular sector.

The area of a sector of a circle with a central angle of 9/13 rad is 24 m2. Find the radius of the circle. (Round your answer to one decimal place.)
1 m

* A conical cup is made from a circular piece of paper with radius 8 cm by cutting out a sector and joining the edges as shown below. Suppose = 7/4.

(a) Find the circumference C of the opening of the cup.
C = cm

(b) Find the radius r of the opening of the cup. [Hint: Use C = 2r.]
r = cm

(c) Find the height h of the cup. [Hint: Use the Pythagorean Theorem.]
h = cm

(d) Find the volume V of the cup.
V = cm3

(a) 0.8 rad

Explanation / Answer

1) arc length = 15m

central angle = 5pi/6

applying arc length formula

s = r theta

15 = r * 5pi/6

r = 15*6 / 5pi

r = 5.73 m

radius = 5.73 metres

2a) central angle = 0.8 rad

area = 22

area = 1/2 r^2 theta

22 = 1/2 * r^2 * 0.8

r^2 = 22*2 / 0.8

r^2 = 55

radius = 7.416

b) area = 22

central angle = 160 deg

22 = pi r^2 ( 160/360)

radius = 3.97