# Help needed...thanks

• Apr 15th 2009, 04:14 AM
BabyMilo
Help needed...thanks
The capacity of a small cylindrical tank is 40 litres. A large cylindrical tank is twice as tall as the small tank and it's diameter is three times the diameter of the small tank. Calculate the capacity of the large tank. Thanks.
• Apr 15th 2009, 04:31 AM
Volume of a cylinder is $=V=\pi r^2h$

$V_1=\pi (r_1)^2(h_1)$

$V_2=\pi (r_2)^2(h_2)$

Divide both the equation

$r_2 = 3r_1$

$h_2= h_1$
• Apr 15th 2009, 04:42 AM
BabyMilo
THanks for you respond!

And what would be the answer?
• Apr 15th 2009, 04:53 AM
Quote:

Originally Posted by BabyMilo
pi *r^2*h= volume of smaller

So it's pi*(3r)^2*(2h)=18pi* r^2* h=18 volume of smaller

• Apr 15th 2009, 05:09 AM
BabyMilo
So you are saying 18 is the volume of the smaller cylindrical tank ?
but shouldnt it be 40? as 40 litres= 40cm^3

cant you just tell me the answer?
• Apr 15th 2009, 05:17 AM
Soroban
Hello, BabyMilo!

Quote:

The capacity of a small cylindrical tank is 40 litres.
A large cylindrical tank is twice as tall as the small tank
and it's diameter is three times the diameter of the small tank.
Calculate the capacity of the large tank.

Let $r$ = radius of the small tank.
Let $h$ = height of the small tank.

The volume of the small tank is: . $v \:=\:\pi r^2h\;=\;40$ litres.

The radius of the large tank is: . $R = 3r$
The height of the large tank is: . $H = 2h$

The volume of the large tank is: . $V \:=\:\pi R^2H \:=\:\pi (3r)^2(2h)$

So we have: . $V \;=\;18\underbrace{\pi r^2h }$
. . . . . . . . . $^{\text{This is the volume of the small tank}}$

Therefore: . $V \:=\:18(40) \:=\:720$ litres.

• Apr 15th 2009, 05:23 AM
BabyMilo
Quote:

Originally Posted by Soroban
Hello, BabyMilo!

Let $r$ = radius of the small tank.
Let $h$ = height of the small tank.

The volume of the small tank is: . $v \:=\:\pi r^2h\;=\;40$ litres.

The radius of the large tank is: . $R = 3r$
The height of the large tank is: . $H = 2h$

The volume of the large tank is: . $V \:=\:\pi R^2H \:=\:\pi (3r)^2(2h)$

So we have: . $V \;=\;18\underbrace{\pi r^2h }$
. . . . . . . . . $^{\text{This is the volume of the small tank}}$

Therefore: . $V \:=\:18(40) \:=\:720$ litres.

Very clear, thanks alot!
Oh, one last thing, where did u get the 18 from?

Oh, i see 3^2*2. Thanks the first guy as well!