Math CentralQuandaries & Queries


i have a diagram of cylinder with a height of 1.260m and radius 0.340m
a hemisphere of radius 0.400m is bonded to one end of the cylinder with a constant overlap
of 0.06m between them
a cylinder of radius 0.170m and length 1.280m is bored out of the composite body what is the volume

also the composite body is to be painted i need to calculate the total area
to be covered

could you please have a look
thank you

Hi Lee,

The volume of a cylinder is pi r2 h where r is the radius and h is the height and the volume of a sphere is 4/3 pi r3 where again r is the radius. The volume of your cylinder is then

pi x 0.3402x 1.260 = 0.458 cubic meters.

The volume of your hemisphere is

1/2 x 4/3 x 0.4003 cubic meters

Add these two values and subtract the volume of the cylindrical hole to arrive at the volume remaining.


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