SOLUTION: A <s>cylinda</s> CYLINDER and sphere both have the same diameter and the same volume.if the height of the cylinder is 36cm, find their common radius.

Question 999085: A ~~cylinda~~ CYLINDER and sphere both have the same diameter and the same volume.if the height of the cylinder is 36cm, find their common radius.
Found 2 solutions by addingup, josgarithmetic:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Volumes: cylinder= pi*r^2*h sphere= 4/3pi*r^3
Let's rewrite the cylinder this way: h*pi*r^2
36*pi*r^2= 4/3pi*r^3
subtract 4/3pi*r^3 from both sides
36*pi*r^2-4/3pi*r^3= 0 Now factor the left:
-4/3pi*r^2(r-27)= 0 Divide both sides by -4/3pi to simplify:
r^2(r-27)= 0 (of course, you divided the zero by -4/3pi but zero divided by any number is 0).
Split into 2 equations:
r-27= 0 or r^2= 0 on the left, add 27 on both sides and on the right take the square root on both sides:
Your answer:
r= 27 or r= 0 Throw away the 0, your answer is 27
Proof:
pi*27^2*36= 4/3pi*27^3 Do it in your calculator, I've run out of time but I'm sure you will find that the equality is true, meaning we've got the right answer.
Answer by josgarithmetic(39629) (Show Source): You can put this solution on YOUR website!
Cylinder volume,

Sphere volume, .

If their diameters are equal then also their radii are equal. h=36 for the cylinder.

Their volumes are described as equal.
, both sides contain factor ,...

-------The answer in purely symbolic form.
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