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The radius of a cylinder is half of the side of the square, whose perimeter is 6 cm more than the perimeter of a rectangle. If the ratio between the length and breadth of a rectangle is 7: 2 and between the length of the rectangle and the side of the square is 3 : 2. Find the volume of a cylinder. Given the height of the cylinder is equal to the breadth of the rectangle.

The radius of a cylinder is half of the side of the square, whose perimeter is 6 cm more than the perimeter of a rectangle. If the ratio between the length and breadth of a rectangle is 7: 2 and between the length of the rectangle and the side of the square is 3 : 2. Find the volume of a cylinder. Given the height of the cylinder is equal to the breadth of the rectangle. Correct Answer <p>24948 cm<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">3</span></p>

Given:

Length of rectangle : Breadth of a rectangle = 7: 2

Length of the rectangle : Side of the square = 3 : 2

Perimeter of Square – Perimeter of Rectangle = 6

Concept Used:

Area of Rectangle = Length × Breadth

Volume of Cylinder = πR2 h

R = Radius of Cylinder

h = Height of Cylinder

Calculation:

Ratio of breadth, length and side of square = 2 : 7 ∷ 3 : 2

⇒ (2 × 3) : (7 × 3) : (7 × 2)

⇒ 6 : 21 : 14

Ratio between length, breadth and side of square = 21 : 6 : 14

Let the length and breadth of rectangle be 21x cm and 6x cm respectively.

And, side of the square be 14x cm

According to the question

⇒ 4(14x) – 2(21x + 6x) = 6

⇒ 56x - 54x = 6

⇒ x = 3 cm

Radius of Cylinder = 14 × (3/2)

⇒ 21 cm

Height of Cylinder = 6 × 3

⇒ 18 cm

Volume of Cylinder = πR2h

⇒ (22/7) × 21 × 21 × 18

⇒ 24948 cm3

∴ The volume of cylinder is 24948 cm3.

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