SOLUTION: A lead ball is formed into a circular sheet. Find diameter of sheet. Ball diameter; 2 in. Sheet thickness; 0.01 in. A ball is a sphere. Volume; 4/3 * pi * r^3 Ar

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Question 1128923: A lead ball is formed into a circular sheet. Find diameter of sheet.
Ball diameter; 2 in.
Sheet thickness; 0.01 in.
A ball is a sphere.
Volume; 4/3 * pi * r^3
Area of circle; pi * r^2

4/3 * 3.1416 * 1^3 = 1.3333 * 3.1416 * 1^3 = 4.18869 cu. in.

Unsure how to proceed. Non-homework.
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The circular sheet is a very thin cylinder, with height 0.01 inches.

Volume of lead ball (sphere): %284%2F3%29%28pi%29%28r%5E3%29+=+%284%2F3%29%28pi%29%281%5E3%29+=+%284%2F3%29%28pi%29

Volume of circular sheet (cylinder): %28pi%29%28r%5E2%29%28h%29+=+%28pi%29%28r%5E2%29%280.01%29+=+0.01%28pi%29r%5E2

The two volumes are the same:

%284%2F3%29pi+=+0.01%28pi%29r%5E2%29
4%2F3+=+0.01r%5E2
r%5E2+=+400%2F3
r+=+sqrt%28400%2F3%29 = about 11.55 inches

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A lead ball is formed into a circular sheet. Find diameter of sheet.
Ball diameter; 2 in.
Sheet thickness; 0.01 in.
A ball is a sphere.
=============
Vol of the sphere = 4pi*r^3/3 = 4pi/3 cubic inches.
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Volume of the sheet = pi*r^2*h where h = thickness of 0.01"
V of sheet = pi^r^2*0.01
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The 2 volumes are equal
4pi/3 = pi*r^2*0.01
0.01r^2 = 4/3
r^2 = 400/3
r =~ 11.54"
d =~ 23.09 inches