*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
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
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