22. If per cent increase in radius of a cylinder 3500%, then by how much per cent will the volume of cylinder change (keeping height of cylinder constant)?
Answers
Answer:
Given:
Radius increased by 300% and the height remains constant
Concept Used:
If r be the radius of the base of a cylinder and h be the height of the cylinder then the volume of the cylinder is πr2h
Calculation:
Let r be the radius of the base of the cylinder and h be the height of the cylinder
The volume of the cylinder is πr2h
after increasing the radius by 300% it increased by (300/100)r = 3r
Now length of the new radius is (r + 3r) = 4r
The new volume of the cylinder is π(4r)2h
⇒ 16πr2h
Volume increased by (16πr2h - πr2h) = 15πr2h
Volume increase by the percent is [(15πr2h/πr2h) × 100]%
⇒ 1500%
∴ The volume of the cylinder is increased by 1500%
Answer:
Let r be the radius of the base of the cylinder and h be the height of the cylinder
The volume of the cylinder is πr2h
after increasing the radius by 300% it increased by (300/100)r = 3r
Now length of the new radius is (r + 3r) = 4r
The new volume of the cylinder is π(4r)2h
⇒ 16πr2h
Volume increased by (16πr2h - πr2h) = 15πr2h
Volume increase by the percent is [(15πr2h/πr2h) × 100]%
⇒ 1500%
∴ The volume of the cylinder is increased by 1500%