Question

The radius and height of a cylinder is in ratio 7:3. volume of cylinder is 12475 cm3 .find the radius and height of the cylinder.

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Answer 1

Given that:

• The radius and height of a cylinder is in ratio 7 : 3.
• Volume of cylinder is 12475 cm³.

To Find:

• The radius and height of the cylinder.

Let us assume:

• The radius and height of the cylinder be 7x and 3x respectively.

We know that:

• Volume of a cylinder = πR²h

Where,

• π = Pie = 22/7
• R = Radius = 7x
• h = Height = 3x

Finding the radius and height of the cylinder:

According to the question.

↣ 12475 = π(7x)²(3x)

↣ 12475 = 22/7(7x × 7x)(3x)

↣ 12475 = 22(7x²)(3x)

↣ 12475 = 462x³

↣ 12475/462 = x³

↣ 27.002 = x³

↣ (3)³ = x³

Cancelling power.

↣ 3 = x

↣ x = 3 (approx.)

• Radius = 7x = 7(3) = 21 cm
• Height = 3x = 3(3) = 9 cm

Hence,

• The radius and height of the cylinder are 21 cm and 9 cm respectively.

Answer 2

Given :-

The radius and height of a cylinder is in ratio 7:3. volume of cylinder is 12475 cm³

To Find :-

Radius and height

Solution :-

We know that

Volume of cylinder = πr²h

Let

Radius be 7a

Height be 3a

12475 = π × (7a)² × 3a

12475 = 22/7 ×  49a² × 3a

12475 = 22 × 7a² × 3a

12475/22 = 21a³

579.31 = 21a³

579.31/21 = a³

27 ≈ a³

∛27 = a

3 = a

Hence

Radius

⇒ 7a

⇒ 7(3)

⇒ 21 cm

Height

⇒ 3a

⇒ 3(3)

⇒ 9 cm