Ball Volume
Ball Volume
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thickness of a ball- volume- geometry?
a hollow steel ball has a diameter of 14 inches and weighs 327.36 pounds. steel has a density of .28 pounds per cubic inch. how do i find the thickness of the ball?
weight density = weight/ volume
solving for volume
volume = weight/weight density
v = 327.36 #'s/ 0.28 #'s per cu.in
= 1169.142857 cu.in (volume of the hollow steel ball)
but,
v = volume of whole steel ball - volume of the hollow part
= 4/3 pi r^3 - 4/3 pi (r1)^3
=4/3 pi 7^3 - 4/3 pi (7-t)^3
= 4/3 pi [ 7^3 -(7-t)^3]
1169.142857 = 4/3 pi [ 7^3 -(7-t)^3]
multiply 3 and divide 4 pi on both sides
3/(4 pi) (1169.142857) = 7^3 - (7-t)^3
subtract 3/4pi (1169.142857) and add (7-t)^3 on both sides
(7-t)^3 = 7^3 - 3/4 pi [1169.142857]
(7-t)^3 = 63887
get the cube root of both sides
7- t = 3.997
substract 3.997 and add t on both sides
t = 7 - 3.997
= 3.003 inches
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