srmessi wrote:
The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3\). A solid sphere of radius r that is made of a certain material weighs 40 pounds.
The figure above shows half of a spherical shell made of the same material.
What is the weight, in pounds, of the entire spherical shellif the outer radius is 5r and the inner radius is 2r?
A. 120
B. 360
C. 840
D. 1,080
E. 4,680
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\(\frac {4}{3} \pi r^3\) = \(40\)
\(\frac{22}{7} r^3\) = \(30\)
\(\frac{11}{7} r^3\) = \(15\)
\(r^3\) = \(15*7/11\)
Now think about the semi circle
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Circle.PNG [ 13.33 KiB | Viewed 59340 times ]
So, Volume will be = \(\frac{2}{3}*\frac{22}{7}*( 5r^3 - 2r^3)\)
Or Volume = \(\frac{2}{3}*\frac{22}{7}*( 117r^3)\)
We know r^3 = \(15*7/11\) ; so substitute it ....Volume = \(\frac{4}{3}*\frac{22}{7}*( 117*15*\frac{7}{11})\)
( Check the highlighted part in the question we require the volume of the complete sphere )Volume = 4,680You may ask the question why the question mentions
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The figure above shows half of a spherical shell
It's given only to show that the thickness of the spherical ball (which is hollow from inside )
Hence I completely endorse answer option (E) _________________