Cones A and B both have volume 48 cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B. Explain how you know Cone B has the same volume as Cone A.
Answers
Given : Cones A and B both have volume 48 cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units.
To Find : possible radius and height for Cone B.
Solution:
Volume of cone = (1/3)πR²H
Volume of cone A = (1/3)π6²*4 = 48π cubic units
Volume of cone B = (1/3)πr²*h = 48π cubic units
(1/3)πr²*h = (1/3)π6²*4 =
=> r²*h = 6²*4 = 144
6 has factor 1 , 2 , 3
r = 1
=> 1²*h = 144 => h = 144
r = 2
=> 2²*h = 144 => h = 36
r = 3
=> 3²*h = 144 => h = 16
Also integral possible values of r :
r = 4
=> 4²*h = 144 => h = 9
r = 6
=> 6²*h = 144 => h = 4
r = 12
=> 12²*h = 144 => h = 1
Possible integral values of cone B
r = 1 , h = 144
r =2 , h = 36
r = 3 , h = 16
r = 4 , h = 9
r = 6 , h = 4 ( Cone A)
r = 12 , h = 1
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