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# A tank has the shape of a cylinder with hemispherical ends.

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A tank has the shape of a cylinder with hemispherical ends.  If the cylindrical part is 10m long and has an outside radius of 1m, abaout how much paint is required to coat the outside of the tank to a thickness of 1 millimeter?

Guest May 21, 2017
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We' ll  give the answer in mm^3

Note.....1 m   =   1000mm      and 10m  =  10000 mm

The volume  of the tank (without the paint)  =

(4/3) pi (1000mm) ^3  +  pi (1000mm)^2 (10000mm)         (1)

The volume of the tank (including the paint)  =

(4/3)pi (1001mm)^3  + pi (1001mm)^2 (10000m)       (2)

So.....the volume of paint required   =  (2)  - (1)  =

(4/3)pi [ 1001^3 - 1000)^3]  +  (10000)pi [1001^2 - 1000^2] =

(12012004 π)/3  + 20010000 π    ≈  75,442,210  mm^3

CPhill  May 21, 2017

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