1. ## 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.

2. Volume of a cylinder is $\displaystyle =V=\pi r^2h$

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

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

Divide both the equation

$\displaystyle r_2 = 3r_1$

$\displaystyle h_2= h_1$

3. THanks for you respond!

And what would be the answer?

4. 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

5. 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?

6. Hello, BabyMilo!

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

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

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

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

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

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

7. Originally Posted by Soroban
Hello, BabyMilo!

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

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

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

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

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

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