Find the percentage of wastage material in converting a cylinder of base diameter 10 cm and height 20 cm into a cone of equal base, but double the height of the cylinder.

Correct option is B

Given:

Base diameter of the cylinder = 10 cm

Height of the cylinder = 20 cm

Height of the cone = 40 cm (double the height of the cylinder)

Formula Used:

The volume of a cylinder is given by cylinder = $$π r^2 \times h$$​, where r is the radius and h is the height.

The volume of a cone is given by cone =$$(1/3) \times π \times r^2\times h$$​ where r is the radius and H is the height.

Solution:

The volume of the cylinder:

Radius of the base = 10/2 = 5 cm

Height of the cylinder = 20 cm

Volume of the cylinder = $$π \times 5^2 \times 20$$​ = 500π cubic cm

The volume of the cone:

Height of the cone = 40 cm

Volume of the cone = $$(1/3) \times π \times 5^2 \times 40$$​ = (1000π)/3 cubic cm

Percentage of wastage material:

Wastage = Volume of the cylinder - Volume of the cone

Wastage = 500π - (1000π)/3 = (1500π)/3 - (1000π)/3 = (500π)/3 cubic cm

Percentage of wastage = ({500π/3}/ 500π) ×100 = (1/3) ×100 = 33.33%