Question

The perimeter of the base of a
right circular cylinder is 'a
unit. If the volume of the cyl-
inder is V cubic unit, then the
height of the cylinder is​

Answer 1

Given :-

• perimeter of the base of a right circular cylinder = a
• volume of the cylinder = V cubic unit

To find :

• the height of the cylinder

Formula used :

• Volume of cylinder = π r² h

• Perimeter/ circumference of base of cylinder = 2π r

where :-

• r = radius of base of cylinder

• h = height of cylinder

Solution :

perimeter/ circumference of the base of a right circular cylinder = a

We know that:- circumference = 2π r

therefore :-

⟶ a = 2π r

⟶ 2π r = a

⟶ r = a/2π

Therefore radius = a/2π ( where a = circumference of base of cylinder)

⟶ volume of the cylinder is given as = V cubic unit

⟶ Volume of cylinder = π r² h

Therefore, according to the question :-

⟶ V = π r² h

put : r = a/2π

⟶ V = π (a/2π)² h

⟶ V = π × (a/2π) × (a/2π)×h

⟶ V = (π/π) × (a/2) × (a/2π)×h

⟶ V = (a²/4π) ×h

⟶ 4π V /a² = h

Answer :

The height of the cylinder = 4π V /a² unit

__________________________

Learn more :

• Volume of cylinder = πr²h

• T.S.A of cylinder = 2πrh + 2πr²

• Volume of cone = ⅓ πr²h

• C.S.A of cone = πrl

• T.S.A of cone = πrl + πr²

• Volume of cuboid = l × b × h

• C.S.A of cuboid = 2(l + b)h

• T.S.A of cuboid = 2(lb + bh + lh)

• C.S.A of cube = 4a²

• T.S.A of cube = 6a²

• Volume of cube = a³

• Volume of sphere = 4/3πr³

• Surface area of sphere = 4πr²

• Volume of hemisphere = ⅔ πr³

• C.S.A of hemisphere = 2πr²

• T.S.A of hemisphere = 3πr²

___________________