SOLUTION: Find the volume of material that is needed to form a spherical shell whose outer radius is 6.0 inches and whose thickness is 0.01 inches. Use your answer to estimate the surface ar

Algebra ->  Formulas -> SOLUTION: Find the volume of material that is needed to form a spherical shell whose outer radius is 6.0 inches and whose thickness is 0.01 inches. Use your answer to estimate the surface ar      Log On


   

Question 149517: Find the volume of material that is needed to form a spherical shell whose outer radius is 6.0 inches and whose thickness is 0.01 inches. Use your answer to estimate the surface area of the 6-inch sphere.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the volume of the outer sphere. Note: I'm going to call this volume V%5Bo%5D


V=%284%2F3%29pi%2Ar%5E3 Start with the volume of a sphere formula.


V%5Bo%5D=%284%2F3%29pi%2A%286%29%5E3 Plug in r=6


V%5Bo%5D=%284%2F3%29pi%2A%28216%29 Cube 6 to get 216


V%5Bo%5D=904.77868 Multiply.


So the volume of the outer sphere is V%5Bo%5D=904.77868


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Now let's find the volume of the inner sphere. Since the shell is 0.01 inches thick, this means that the inner radius is 6-0.01=5.99 inches.

Note: I'm going to call this volume V%5Bi%5D


V=%284%2F3%29pi%2Ar%5E3 Start with the volume of a sphere formula.


V%5Bi%5D=%284%2F3%29pi%2A%285.99%29%5E3 Plug in r=5.99


V%5Bi%5D=%284%2F3%29pi%2A%28214.92%29 Cube 5.99 to get 214.92


V%5Bi%5D=900.26232 Multiply.


So the volume of the inner sphere is V%5Bi%5D=900.26232


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So to find the volume of the shell, simply subtract the volume of the inner sphere is V%5Bi%5D from the volume of the outer sphere is V%5Bo%5D like this

V%5Bo%5D-V%5Bi%5D=904.77868-900.26232=4.51636


So the volume of the shell is about 4.52 cubic inches


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To find the surface area of the outer sphere, simply use this formula A=4pi%2Ar%5E2


A=4pi%2Ar%5E2 Start with the surface area formula


A=4pi%2A%286%29%5E2 Plug in r=6


A=4pi%2A%2836%29 Square 6 to get 36


A=144pi Multiply


So the surface area of the outer sphere is A=144pi which is approximately 452.39 square inches.