MHB Calculating Volume of a Solid by Subtracting Volumes of Basic Shapes

[mathlearn]

Please solve this problem

View attachment 5776

:)

 

[SuperSonic4]

Please solve this problem

:)

Good evening and welcome to MHB! :D

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Can you post what you have done so far?

 

[mathlearn]

Thank you super Sonic

So far

I calculated the volume of the cyclinder by taking "a" as the radius π(pie)a^2h

and I calculated the volume of the hemisphere (4/3πr^3)

and that was so far

 

[MarkFL]

Okay, using your formulas, we have the volume of a cylinder having radius $a$ as:

$$V_C=\pi a^2h$$

And the volume of a hemisphere of radius $a$ as:

$$V_H=\frac{2}{3}\pi a^3$$

Now, in order to find the volume of the given solid, we need to take the volume of the cylinder and remove (subtract) the volume of the hemisphere:

$$V_S=V_C-V_H$$

So, plug in for $V_C$ and $V_H$, then factor...what do you get?