SOLUTION: A can has a diameter of 3in. And a height of 5in. Explain whether doubling the height of the can would have the same effect on the volume as doubling the diameter

Algebra ->  Volume -> SOLUTION: A can has a diameter of 3in. And a height of 5in. Explain whether doubling the height of the can would have the same effect on the volume as doubling the diameter      Log On


   

Question 857462: A can has a diameter of 3in. And a height of 5in. Explain whether doubling the height of the can would have the same effect on the volume as doubling the diameter
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Translate the description completely into symbols and see what happens.

volume of a right circular cylinder, h%2Api%2A%28d%2F2%29%5E2;
h is length top to bottom;
d is diameter
And simplifying the expression,
highlight%28%281%2F4%29h%2Api%28d%5E2%29%29-----for our original cylinder.

Doubling the height, which I have called "length" as h:
volume becomes 2h%2Api%2A%28d%2F2%29%5E2
Simplifying,
2h%2Api%28d%5E2%29%2F%282%2A2%29
highlight%28%281%2F2%29h%2Api%28d%5E2%29%29-----Cylinder when doubled height.

Starting again with original cylinder, Doubling the Diameter:
h%2Api%282d%2F2%29%5E2
Simplifying,
highlight%28h%2Api%28d%5E2%29%29--------Cylinder when doubled diameter.

Now you can more easily analyze how doubling the height or doubling the diameter affects the volume of the original cylinder. You will find that each of the resulting expressions contain the same factor, h%2Api%2Ad%5E2.