Author Topic: [HELP] Stuck on a question! (Read 2197 times) Tweet Share

tzacchary · « **on:** April 21, 2014, 09:28:46 pm »

I'm stuck!
Any help?

A container has a cylindrical base and a hemispherical
top as shown in the figure at right. The height of the
container is 20 cm and its capacity is to be exactly
2 litres. Let r cm be the radius length of the base.
20 cm
r cm
a Express the height of the cylinder in terms of r. (Done this one, answer is 20-r)
b i Express the volume of the container in terms of r.
ii Find r and h if the volume is two litres.
(Stuck on those two! Image of the question attached! And here's an imgur link just to be safe: http://i.imgur.com/O06YqtG.png)

Thanks so much guys!

Conic · « **Reply #1 on:** April 21, 2014, 09:48:16 pm »

The volume for half a sphere is $\frac{2}{3} \pi r^3$ , and the volume of a cylinder is $\pi r^2 h$ . So the total volume of the container is given by:

$V_{container}=\frac{2}{3} \pi r^3 + \pi r^2 h$

$=\frac{2}{3} \pi r^3 + \pi r^2 (20-r)$

$=\frac{2}{3} \pi r^3 + 20 \pi r^2 - \pi r^3$

$=20 \pi r^2- \frac{1}{3} \pi r^3$

$=\left (20r^2-\frac{r^3}{3}\right )\pi$

Then you can solve $V_{container}=2000$ (as 1L=1000cm^3) to find the radius for the next part.

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Author Topic: [HELP] Stuck on a question! (Read 2197 times) Tweet Share

tzacchary

[HELP] Stuck on a question!

Conic

Re: [HELP] Stuck on a question!

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