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Two cones have the same volume. If one has a base with radius 3 times as large as the other's and a height of 24 inches, how many inches tall is the other?

Note: The volume of a cone is \(\frac{1}{3} \pi r^2 h,\) where r is the radius and h is the height.

 Jul 16, 2020
 #1
avatar+1130 
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we have the expression (3x)^2*24=x^2*y we solve that (3x)^2=9x^2 and 9x^2 is and 9x^2 is 9 times x^2 so the height of the other cone is y=27*9=216 inches and our final answer is 216 inches

 Jul 16, 2020
edited by jimkey17  Jul 16, 2020
 #4
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We cancel out the 1/3 and the 𝝅 so we have this

jimkey17  Jul 16, 2020
 #7
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R = 3             r = 1

 

1/3 * pi * 32 * 24 = 1/3 * pi * 12 * h

 

226.1946711 = 1.047197551 * h

 

h = 216  surprisesmiley

Guest Jul 16, 2020
 #8
avatar+1130 
+2

oops I divided but it was supposed to be multiplied thanks Guest

jimkey17  Jul 16, 2020
 #6
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Believe it or not, the height of the other cone is 216 inches!!!  frown

 Jul 16, 2020

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