SOLUTION: Two similar cones have heights 5 and 10. What is the ratio of their volumes? I am graduating in two weeks and I'm getting so nervous, I know this is probably staring at me in face

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Question 155812: Two similar cones have heights 5 and 10. What is the ratio of their volumes? I am graduating in two weeks and I'm getting so nervous, I know this is probably staring at me in face with an answer, but I just can't figure out the formula or whatever it takes this is for a test. If you can help me this would take so much pressure off my brains. Thank you!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Two similar cones have heights 5 and 10. What is the ratio of their volumes?
.
Several things you need to "bring" to bear on this problem.
1. The fact that it is a "similar" cone should tell you that all its measurements are in proportion.
2. The volume of a cone is: V = hB/3
where
h is the height
B is the area of the base
3. Area of a circle is: (pi)r^2
.
If we let r = radius of smaller cone then
Because the problem tells us: "Two similar cones have heights 5 and 10" we can NOW say the radiis are "r" and "2r".
.
Volume of smaller cone:
hB/3
5(pi)(r^2)/3
.
Volume of larger cone:
hB/3
10(pi)(4r^2)/3
.
Finally, the ratio of their volumes:
[5(pi)(r^2)/3]/[10(pi)(4r^2)/3]
multiplying numerator and denominator by 3:
[5(pi)(r^2)]/[10(pi)(4r^2)]
dividing numerator and denominator by pi:
[5(r^2)]/[10(4r^2)]
dividing numerator and denominator by r^2:
[5]/[10(4)]
dividing numerator and denominator by 5:
[1]/[2(4)]
finally, resulting in:
1/8