Question

The cylinder and cone have the same radius and height.
The Total Volume is 500cm^3.
What is the Volume of the Cylinder?
What is the Volume of each Cone?

Answer 1

Answer:

Volume of Cylinder = 300cm^3, Volume of 1 Cone = 100cm^3

Step-by-step explanation:

Let r be the radius

Let h be the Height

Given r = h, we will take h as r.

Volume of cylinder  $\pi r^{2} h\\=\pi r^{2} (r)\\=\pi r^{3}$

Volume of 2 cones  $2(\pi r^{2} \frac{h}{3} )\\=2(\pi r^{2} \frac{r}{3} )\\= 2(\frac{\pi r^{3} }{3} )\\=\frac{2}{3} \pi r^{3}$

Given Total Volume = 500cm^3 = Volume of cylinder + Volume of 2 cones

$\pi r^{3} + \frac{2}{3}\pi r^{3} = 500 \\\frac{5}{3} \pi r^{3} = 500\\\pi r^{3} = 500*\frac{3}{5} \\\pi r^{3} = 300\\r^{3} = \frac{300}{\pi } \\r=\sqrt[3]{\frac{300}{\pi } } cm$

Now we got r and r=h,

Volume of Cylinder  $\pi (\sqrt[3]{\frac{300}{\pi } } )^{3}\\=\pi (\frac{300}{\pi } )\\= 300cm^{3}$

Volume of 1 cone = (Total Volume - Volume of Cylinder) / 2

= (500-300)/2

= 200/2

= 100cm^3