Question

Two similar cylindrical cans hold 2 litres and 6.75 litres of liquid. If the diameter of the smaller can is 16cm, find the diameter of the larger can.

Answer 1

Explanation:

It is given that,

Volume of the cylindrical can 1 is 2 litres and that of cylindrical can 2 is 6.75 litres. The diameter of the smaller can is 16 cm. We need to find the diameter of the larger can.

The formula of the volume of a cylinder is given by :

`V=\pi r^2h`

So,

`(V_1)/(V_2)=(r_1^2)/(r_2^2)`

Diameter, d = 2r

`(V_1)/(V_2)=((d_1/2)^2)/((d_2/2)^2)\\\\(V_1)/(V_2)=((d_1^2)/(d_2^2))`

V₁ = 2 L, V₂ = 6.75 L, d₁ = 16 cm, d₂ = ?

`(2)/(6.75)=((16^2)/(d_2^2))\\\\d_2=29.39\ cm`

So, the diameter of the larger can is 29.39 cm.