+0  
 
0
62
2
avatar

A sector with radius 10 and central angle $45^\circ$ is to be made into a right circular cone. Find the volume of the cone.

 Jan 24, 2021
 #1
avatar+116126 
+1

The slant  height of the  cone will  be  =   10

 

The circumference of the  cone =    2pi *10  (45/360)  = 2.25 pi   =    2pi r

 

The radius  of the  cone =  2.25/2  =  9/8  =1.125

 

The  height of the  cone  = sqrt   (10^2  -1.125^2 )   

 

The volume of the  cone   =

 

pi * r^2  * height /  3   =

 

pi  * (1.125)^2  * sqrt   (10^2  - 1.125^2)   / 3    ≈   13.17 units^3

 

 

 

cool cool cool

 Jan 24, 2021
 #2
avatar
+1

A sector with a radius of 10 and a central angle of 45º is to be made into a right circular cone. Find the volume of the cone.

("central angle of 45º "   means that a sector of 45º is cut out and the remaining (larger) sector is used to make a cone.)

 

Circle radius = 10      (this is also the slant height of a cone)

 

Cone radius = 10(315/360)     r = 8.75

 

Cone height     h = sqrt(102 - 8.752) = 4.841229183

 

Cone volume      V = pi * r2 * h/3        V ≈ 388.15 square units

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The question calls for the right cone; let's check if it's a right cone.

 

102 = 8.752 + 4.8412291832

 

100 = 100    correct!!! smiley

Guest Jan 25, 2021

50 Online Users

avatar
avatar
avatar
avatar
avatar
avatar