Question

A cylindrical container with a radius of 5 cm and a height of 14 cm is completely filled with liquid. Some of the liquid from the cylindrical container is poured into a cone–shaped container with a radius of 6 cm and a height of 20 cm until the cone–shaped container is completely full. How much liquid remains in the cylindrical container? (1 cm3 = 1 ml)

Answer 1

Volume left in the cylinder if all the cone is made full:

`\bold{345.72 \ ml }`

Explanation:

Given

Radius of cylinder = 5 cm

Height of cylinder = 14 cm

Radius of cone = 6 cm

Height of cone = 20 cm

To find:

Liquid remaining in the cylinder if cone is made full from cylinder's liquid.

Solution:

We need to find the volumes of both the containers and find their difference.

Volume of cylinder is given by:

`V_(cyl) = \pi r^2h`

We have r = 5 cm and

h = 14 cm

`V_(cyl) = (22)/(7) * 5^2* 14 = 1100 cm^3`

Volume of a cone is given by:

`V_(cone) = (1)/(3)\pi r^2h = (1)/(3)* (22)/(7) * 6^2 * 20 = (1)/(3)* (22)/(7) * 36 * 20 = 754.28 cm^3`

Volume left in the cylinder if all the cone is made full:

`1100-754.28 =345.72 cm^3\ OR\ \bold{345.72 \ ml }`