Bronze Challenge
Geometry challenge for the Math geniuses out there!?
Please show your steps accurately.
A metal sculptor has a solid bronze sphere wih a radius of 10 in. She melts the sphere and casrs a hollow sphere with an inner radius of 10 in. What is the thickness of the shell of the hollow sphere?
Thank you
The material available is the volume of the original sphere
V = 4/3(pi)r^3 = 4000pi/3
The amount of material used in the 2nd sphere is the volume
of a sphere with radius 10 + t (where t is the thickness we are after)
minus the volume of the hole in the middle = 4000pi/3
so we have that
4000pi/3 = 4pi/3 x (10+t)^3 – 4000pi/3
dividing everything by 4pi./3 changes this to
1000 = (10+t)^3 – 1000 or
(10+t)*3 = 2000
take cube root of both sides to get
10 + t = 12.599
so t = 2..59
NFSC – Bronze Challenge #3 Checkpoint
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