What is the volume of the item described?
a capsule consisting of a cylinder of radius 3 mm and height 6 mm with a hemisphere on each end of radius 3 mm.
select the exact answer in terms of π and the approximate answer rounded to the nearest whole number.

254mm^3
90mm^3
54mm^3
170mm^3
81mm^3
283mm^3

*choose more than one*

Step 1

Find the volume of the cylinder

we know that

The volume of a cylinder is equal to

where

r is the radius of the cylinder

h is the height of the cylinder

we have

substitute  the values

Step 2

Find the volume of the two hemisphere

we know that

two hemisphere is equal to one sphere

The volume of the sphere is equal to

where

r is the radius of the sphere

we have

substitute

Step 3

Find the volume of the capsule

we know that

the volume of the capsule is equal to the volume of a cylinder plus the volume of the two hemisphere

so

therefore

the answer is

The volume of a capsule is

The volume of a capsule is

both equations and proportions are better.