Question

A conical flask is full of water. The flask has base radius r and height h. The water is poured into a cylindrical flask of base-radius mr. Find the height of water in the cylindrical flask.

Answer 1

Given base radius of conical flask be r

Height of conical flask is h

Volume of cone = `1/3pir^2h`

So its volume = `1/3pir^2h`  ........(1)

Given base radius of cylindrical flask is ms.

Let height of flask be h₁

Volume of cylinder =`pir^2h_1`

So its volume =`22/7(mr)^2xxh_1`    .........(2)

Since water in conical flask is poured in cylindrical flask their volumes are same

(1) = (2)

⇒`1/3pir^2h = pi(mr)^2xxh_1`

⇒ `h_1 = h/(3m^2)`

∴Height of water in cylindrical flask = `h/(3m^2)`