Question

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42cm and height 21cm which are filled completely. Find the diameter of cylindrical vessel?

Answer 1

Given that diameter is equal to height of a cylinder

so h = 2π

Volume of cylinder=πr²h

So volume = πr²(2r)

2πr³

Volume of each vessel =πr²h

Diameter = 42cm

Height = 21cm

Diameter(d) = 2r

2r = 42

r = 21

∴ Radius = 21cm

Volume of vessel = π(21)²x21                ...........(2)

Since volumes are equal

Equating (1) and (2)

⇒ 2πr³= π(21)² x 21 x 2            (∵ 2 identical vessels)

⇒ `r^2=(pi(21)^2xx21xx2)/(2xxpi)` 

⇒ r³ = (21)³

⇒ r = 21 ⇒ d = 42cm

∴ Radius of cylindrical vessel = 21cm 
Diameter of cylindrical vessel= 42 cm.