SOLUTION: 1 solid is a sphere and has a radius of 6 in the other solid is a cylinder with a radius of 6 in and a height of 6 in what is the difference the volumes have
in
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Question 1190570: 1 solid is a sphere and has a radius of 6 in the other solid is a cylinder with a radius of 6 in and a height of 6 in what is the difference the volumes have
in
Found 3 solutions by josgarithmetic, math_tutor2020, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
You know or can find the formulas for volume of sphere and cylinder?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
V = (4/3)*pi*r^3 .... volume of a sphere
V = (4/3)*pi*6^3
V = 288pi
The sphere has an exact volume of 288pi cubic inches.
V = pi*r^2*h .... volume of a cylinder
V = pi*6^2*6
V = 216pi
The cylinder has an exact volume of 216pi cubic inches
The difference of the volumes is
sphere - cylinder = 288pi - 216pi = 72pi cubic inches
Extra info:
The ratio of the volumes is
cylinder/circle = (216pi)/(288pi) = 3/4
meaning that the cylinder is exactly 3/4 the volume of the sphere
cylinder volume = (3/4)*(sphere volume)
This only works if r = h, and r is the same for both the sphere and cylinder.
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.
This discovery is attributed to Archimedes, a great ancient Greece mathematician, physicist and engineer (c. 287 - c. 212 BC).
He was first who discovered that in this situation
volume of the cylinder is equal to the volume of the inscribed sphere PLUS the volume of the inscribed cone with the same base.
The legend says that Archimedes bequeathed to carve this formula on his grave.
About Archimedes, read this Wikipedia articles
https://en.wikipedia.org/wiki/Archimedes
https://simple.wikipedia.org/wiki/Archimedes
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