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.

Printable View

- Apr 15th 2009, 04:14 AMBabyMiloHelp 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 AMADARSH
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

$\displaystyle r_2 = 3r_1$

$\displaystyle h_2= h_1$ - Apr 15th 2009, 04:42 AMBabyMilo
THanks for you respond!

So it's pi*3r^2*2h=answer?

I dont quite get your equation, please explain it further!

And what would be the answer? - Apr 15th 2009, 04:53 AMADARSH
- Apr 15th 2009, 05:09 AMBabyMilo
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 AMSoroban
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 $\displaystyle r$ = 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.

- Apr 15th 2009, 05:23 AMBabyMilo