Question

A piece of paper has a

rectangle ABCD in which
AB - 10cm and BC = 22 cm,
it was folded to form a
right circular cylinder
such that AB is Cincident
to DC Find the volume of
the resulted cylinder​

Answer 1

The volume of the resulting cylinder is 385 cm³

Explanation:

The formula of the rule of a cylinder is V = π r² h, where

• r is the radius of its base

• h is the height of it

When a rectangular paper folded to form a cylinder, then one of its dimension will be the circumference of the base and the other dimension will be the height of the resulted cylinder

∵ ABCD is a rectangle

∵ It is folded where AB coincides with DC

∴ AB is the height of the resulted cylinder

∴ BC is the circumference of the base of the resulted cylinder

∵ AB = 10 cm

∴ h = 10 cm

∵ BC = 22 cm

∴ The circumfrence of the base = 22 cm

∵ The circumference of a circle = 2 π r

→ Equate the rule by 22 to find r

∴ 2 π r = 22

∵ π =
`(22)/(7)`

∴ 2 ×
`(22)/(7)` × r = 22

∴
`(44)/(7)` r = 22

→ Divide both sides by
`(44)/(7)`

∴ r = 3.5 cm

→ Use the formula of the volume above to find the volume of the cylinder

∵ V =
`(22)/(7)` × (3.5)² × (10)

∴ V = 385 cm³

∴ The volume of the resulted cylinder is 385 cm³