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

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) (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

Start with the volume of a sphere formula.

Plug in

Cube 6 to get 216

Multiply.

So the volume of the outer sphere is

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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 inches.

Note: I'm going to call this volume

Start with the volume of a sphere formula.

Plug in

Cube 5.99 to get 214.92

Multiply.

So the volume of the inner sphere is

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So to find the volume of the shell, simply subtract the volume of the inner sphere is from the volume of the outer sphere is like this

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

Start with the surface area formula

Plug in

Square 6 to get 36

Multiply

So the surface area of the outer sphere is which is approximately 452.39 square inches.

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