Math, asked by 12388019, 2 months ago

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

Answered by amitnrw
1

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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