Geo. Apps. of Calculus (1 Viewer)

[DJel]

Hi,

I am stuck on the first part in the following question;

http://img113.imageshack.us/my.php?image=mathsqfw2.png

Any hints on how to find h would be great, I'd prefer to work out the entire question by myself.

I can work out parts two and three, however I am stumped on part one.

Thanks,

DJel.

 

[lyounamu]

Hi,

I am stuck on the first part in the following question;

http://img113.imageshack.us/my.php?image=mathsqfw2.png

Any hints on how to find h would be great, I'd prefer to work out the entire question by myself.

I can work out parts two and three, however I am stumped on part one.

Thanks,

DJel.

1. First prove that the smaller triangle (with 6-h with h) is similar to the larger one with (20 and 6).
2. Then say h/20 = (6-r)/6 (corresponding sides are in same ratio).
3. Once you found h, substitute the value in to find the volume of cylinder (2 x pi x r^2 x h)

EDIT: Then you will prove that the v = .... (shown in the question).
Good luck!!!

 

[pLuvia]

Use the fact there are two triangles, using similar triangles you can work out an expression for h

Spoiler

(20-h)/r=20/6

 

[DJel]

I can't believe I didn't pick that up. Thanks for the help lyounamu and pLuvia.

BTW, lyounamu, the volume of a cylinder is pi x r^2 x h.

DJel.

 

[lyounamu]

I can't believe I didn't pick that up. Thanks for the help lyounamu and pLuvia.

BTW, lyounamu, the volume of a cylinder is pi x r^2 x h.

DJel.

Glad you worked that out. Good luck in you future studies.

 

[DJel]

Glad you worked that out. Good luck in you future studies.

You too.