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

User Sanjeev
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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 ;)

User Grasesed
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