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

Answer:

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

$\bold{345.72 \ ml }$

Step-by-step 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

$V_{cyl} = \dfrac{22}{7} \times 5^2\times 14 = 1100 cm^3$

Volume of a cone is given by:

$V_{cone} = \dfrac{1}{3}\pi r^2h = \dfrac{1}{3}\times \dfrac{22}{7} \times 6^2 \times 20 = \dfrac{1}{3}\times \dfrac{22}{7} \times 36 \times 20 = 754.28 cm^3$

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

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