The height of a cylinder is 2/3rd of its diameter. Its volume is equal to the volume of a sphere whose radius is 4 cm. What is the curved surface area (in cm2) of the cylinder?

112 π/3
32 π
128 π/3
40 π

LohaHridoy

7 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 3 : 128 π/3

Let radius of cylinder be 3x

Diameter of cylinder = 2 × 3x = 6x

Height of the cylinder = 6x × 2/3 = 4x

Radius of sphere R = 4 cm

As we know,

Volume of cylinder = πr²h

Volume of sphere = 4/3 πR³

Curved surface area of cylinder = 2 πrh

According to the question

πr²h = 4/3 πR³

3x × 3x × 4x = 4/3 × 4 × 4 × 4

x³ = (4 × 4 × 4)/(3 × 3 × 3)

x = ∛(4 × 4 × 4)/(3 × 3 × 3) = 4/3

Curved surface area of cylinder = 2 πrh = 2π × 3x × 4x = 2π × 3 × 4/3 × 4 × 4/3 = 128 π/3

7 views Answered 2022-09-04 04:29

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