SOLUTION: A small cone has dimensions of 4m radius, and 10m height. The larger cone's dimensions are unknown, but it is 125 times larger than small cone's volume. How can I find the radi

Question 996457: A small cone has dimensions of 4m radius, and 10m height.
The larger cone's dimensions are unknown, but it is 125 times larger than small cone's volume.
How can I find the radius and the height of the larger cone? using the information given.
I tried multiplying the radius and height by 125 but it was wrong :/
please help!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the small cone has 4m radius and 10m height.

volume of a cone formula is 1/3 * pi * r^2 * h

the volume of the small cone is 1/3 * pi * 4^2 * 10.

now the volume of the large cone is equal to 125 times the volume of the small cone.

this can be shown as v(large) = 125 * 1/3 * pi * 4 * 4 * 10.

if you want to keep the proportions correct, you need to apply the same factor to each of the factors of radius and height.

since there are 3 factors (4*4*10), then you need to take the cube root of 125 and apply that to each of them.

you will get:

v(large) = 1/3 * pi * (125^(1/3) * 4) * (125^(1/3) * 4) * (125^(1/3) * 10).

since 125^(1/3) = 5, you get:

v(large) = 1/3 * pi * (5 * 4) * (5 * 4) * (5 * 10), which becomes:

v(large) = 1/3 * pi * 20 * 20 * 50.

the new radius is 20 and the new height is 50.

the large cone dimensions are in proportion with the small cone dimensions.

the volume of the new cone is 1/3 * pi * 20^2 * 50 = 20000/3

the volume of the small cone is 160/3.

the volume of the large cone is 20000/3.

the volume of the new cone is 125 times the volume of the old cone because 20000 / 125 = 160.

basically, you multiplied each component of the small cone by the cube root of 125.

4 * 125^(1/3) = 4 * 5 = 20

10 * 125^(1/3) = 10 * 5 = 50

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