Question

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
90
`\pi`mm^3
54
`\pi`mm^3
170mm^3
81
`\pi`mm^3
283mm^3

*Choose more than one*

Answer 1

`V_c=54\pi\ mm^(3)`

`V_s=36\pi\ mm^(3)`

`V=90\pi mm^3=283\ mm^(3)`

Explanation:

Given : A capsule consisting of a cylinder of radius 3 mm and height 6 mm with a hemisphere on each end of radius 3 mm.

To find : What is the volume of the item described?

Solution :

First we find the volume of the cylinder,

The volume of a cylinder is

`V_c=\pi r^(2) h`

where,

r is the radius of the cylinder = 3 mm

h is the height of the cylinder = 6 mm

substitute the values

`V_c=\pi * 3^(2)* 6\\V_c=54\pi\ mm^(3)`

Secondly we find the volume of the two hemisphere,

The volume of the sphere is

`V_s=(4)/(3) \pi r^(3)`

where,

r is the radius of the cylinder = 3 mm

substitute the values,

`V_s=(4)/(3) \pi 3^(3)\\V_s=36\pi\ mm^(3)`

Thirdly we find the volume of the capsule,

The volume of the capsule = The volume of a cylinder + The volume of the two hemisphere

`V=54\pi\ mm^(3)+36\pi\ mm^(3)\\V=90\pi\ mm^(3)`

`V=90* 3.14\ mm^(3)=283\ mm^(3)`

Therefore, Option 2,3 and 6 are correct.

Answer 2

Step 1

Find the volume of the cylinder

we know that

The volume of a cylinder is equal to

`V=\pi r^(2) h`

where

r is the radius of the cylinder

h is the height of the cylinder

we have

`r=3\ mm\\h=6\ mm`

substitute the values

`V=\pi 3^(2) 6=54\pi\ mm^(3)`

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

`V=(4)/(3) \pi r^(3)`

where

r is the radius of the sphere

we have

`r=3\ mm`

substitute

`V=(4)/(3) \pi 3^(3)=36\pi\ mm^(3)`

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

`54\pi\ mm^(3)+36\pi\ mm^(3)=90\pi\ mm^(3)`

`90\pi\ mm^(3)=283\ mm^(3)`

therefore

the answer is

The volume of a capsule is
`90\pi\ mm^(3)`

The volume of a capsule is
`283\ mm^(3)`