Question

Consider a hemisphere with a diameter of 12 mm. Find the volume of the hemisphere in terms of π.

Answer 1

Hello !

Answer:

`\boxed{\sf V_(hemisphere)=144\pi\ mm^3}`

Explanation:

The volume of a sphere is given by the following formula :
`\sf V_(sphere)=(4)/(3)\pi r^3` where r is the radius.

Moreover, we know that the volume of a hemisphere is half the volume of a sphere :
`\sf V_(hemisphere)=(1)/(2) V_(sphere)`

We obtain :
`\sf V_(hemisphere)=(2)/(3)\pi r^3`

Given :

• d = 12mm

`\sf r=(1)/(2) d=(12)/(2) \\\underline{\sf r=6mm}`

Let's substitue r with it value in the previous formula :

`\sf V_(hemisphere)=(2)/(3) \pi* 6^3\\\boxed{\sf V_(hemisphere)=144\pi\ mm^3}`

Have a nice day ;)