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3D Geometry problems
1.

2.

3.

 Mar 26, 2024
 #1
avatar+128794 
+1

1.     2pi r =  6

 

         r  =  6/(2pi)  = 3/pi

 

Volume =  pi (r^2) h  = pi * (3/pi)^2 * 10  = 90 / pi

 

2.  L =  sqrt [ 5^2 + 3^2] = sqrt [ 34]

Lateral surface area of  cone  =  pi ^ r * L   =   pi * 3 * sqrt [34] = 3sqrt (34) pi

Lateral surface area of  cylinder  = 2pi r * h =  2 pi * 3 *5 =  30 pi

A/B  =  [ 3sqrt (34) pi ] / [ 30 pi ] =  [sqrt (34) / 10 ] 

 

3.  Circumference  of  cone =  2pi * 20  * (216/360)  = 24pi

 

radius of cone 

24pi  = 2pi r

24 = 2r

r =12

Height of  cone  = sqrt [ 20^2 - 12^2  ]  = sqrt [ 400 - 144]  =  sqrt 256  =  16

 

Volume  of cone =   (1/3) pi * r^2 * h  =  (1/3) pi (12^2) * 16  =  768 pi

 

 

cool cool cool

 Mar 26, 2024
 #2
avatar+85 
+1

You are correct on all of these!

 Mar 26, 2024

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