A cylinder has a curved surface area equal to 350% of the curved surface area of another cylinder. If their radii are in the ratio 3 : 1, then the volume of the smaller cylinder is approximately _____% of the larger cylinder (the smaller cylinder has its radius and height smaller when compared to the larger).

Question

Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 09 Jul, 2024 Shift 1)

Answer 1

Given:

A cylinder has a curved surface area equal to 350% of the curved surface area of another cylinder.

If their radii are in the ratio 3 : 1

Formula Used:

Volume of cylinder = π r²h

CSA of cylinder = 2π rh

Calculation:

let the radius of larger cylinder and smaller cylinder be 3x and x

Height of both cylinder be h₁ and h₂

A cylinder has a curved surface area equal to 350% of the curved surface area of another cylinder.

⇒ 2π (3x)h₁ = (350/100)2 π(x)h₂

⇒ h₁/h₂ = 3.5/3

⇒ h1/h2 = 7/6

According to the question,

Volume of larger cylinder = π (3x)² × 7

Volume of smaller cylinder = π (x)2 × 6

⇒ π (3x)2 × 7 = π (x)2 × 6

⇒ In percentage = (6/63)× 100

⇒ 9.52

∴ The volume of the smaller cylinder is approximately 9.52% of the larger cylinder.