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1)What is the length of a 100 degree arc in a circle of radius 9?

 

2)A circle is divided into 4 sectors, the ratio of whose areas is 1 : 2 : 3 : 4. What is the central angle of the largest sector in degrees?

 

3)A sector of a circle has a central angle of 80 degrees. If the area of the sector is 32pi, what is the radius of the circle?

 

4)Sixteen times the reciprocal of the number of inches in the circumference of a circle equals the number of inches in the diameter of the circle. What is the number of square inches in the area of the circle?

 

5)A rectangular building is 4 meters by 6 meters. A dog is tied to a rope that is 10 meters long, and the other end is tied to the midpoint of one of the long sides of the building. Find the total area of the region that the dog can reach (not including the inside of the building), in square meters.

FiestyGeco  Feb 11, 2018
 #1
avatar+545 
+3

question 2 -

1+2+3+4=10

360/10=3636*4=144

 

winkwinkwink

lynx7  Feb 11, 2018
edited by lynx7  Feb 11, 2018
edited by lynx7  Feb 11, 2018
 #3
avatar+90141 
+1

Thanks, lynx  !!!!

 

cool cool cool

CPhill  Feb 11, 2018
 #2
avatar+90141 
+3

1)What is the length of a 100 degree arc in a circle of radius 9?

 

We have that

 

Arc Length  =  2 pi radius *   ( 100/ 360)  =   2 pi * 9  * (10/36)  =   18 pi * (5/18)  =

 

5 pi   units

 

 

cool cool cool

CPhill  Feb 11, 2018
 #4
avatar+90141 
+2

3)A sector of a circle has a central angle of 80 degrees. If the area of the sector is 32pi, what is the radius of the circle?

 

Area  =    pi  * radius^2  ( 80 / 360)  =

 

32 pi  =   pi  * radius^2  ( 2/9)           divide out pi

 

32   =   (2/9)  * radius^2       multiply both sides by 9/2

 

32 (9/2)  =  r^2

 

144  = r^2         take the positive root of both sides

 

12  = r

 

 

 

cool cool cool

CPhill  Feb 11, 2018
 #5
avatar+90141 
+1

4)Sixteen times the reciprocal of the number of inches in the circumference of a circle equals the number of inches in the diameter of the circle. What is the number of square inches in the area of the circle?

 

I like this one.....

 

Call the number of inches on the circumference,   I

 

So

 

16/ I  = D  =  2r    ⇒  16/ I  =  2r   ⇒   I   =  16/2r   ⇒   I  =  8/r

 

So.......

 

Circumference in inches =  2 * pi * r

 

8/r  = 2 * pi * r         multiply both sides by r

 

8  = 2 * pi * r^2       divide both sides by  2 pi

 

8 /  [ 2pi ]  =  r^2

 

4/pi  = r^2

 

So....the area  is

 

pi  (r^2)  =

 

pi  ( 4/pi)   =     4 units^2

 

 

cool cool cool

CPhill  Feb 11, 2018
 #6
avatar+90141 
0

5)A rectangular building is 4 meters by 6 meters. A dog is tied to a rope that is 10 meters long, and the other end is tied to the midpoint of one of the long sides of the building. Find the total area of the region that the dog can reach (not including the inside of the building), in square meters.

 

The  dog will  be able to  reach  the area of a semi-circle with a radius of 10 m   as well as two  quarter circles with a radius of  (10 - 3) m  =  7m

 

So.....the total area is

 

(1/2 ) pi  * 10^2    +  (1/4) pi (7)^2  +  (1/4) pi (7)^2  =

 

(1/2) * (10)^2  +  (1/2) pi * (7)^2 =

 

(1/2) pi *  ( 10^2 + 7^2)  =

 

(1/2) pi ( 100 + 49)  =

 

(1/2) pi  (149)  =

 

(149/2) pi   ≈  234.04 m^2

 

 

cool cool cool

CPhill  Feb 11, 2018

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