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Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: A circle whose radius is 56 cm and The Rectangle whose length and breadth are in the ratio 7 ∶ 22 respectively. The area of a circle is equal to the area of a rectangle then calculate the perimeter of the rectangle. Quantity II: A cylinder whose radius is (1/7) of the radius of the circle and the height of the cylinder is twice the radius of the circle and the area of the circle is 154 cm2 then, find the volume of the cylinder.

Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: A circle whose radius is 56 cm and The Rectangle whose length and breadth are in the ratio 7 ∶ 22 respectively. The area of a circle is equal to the area of a rectangle then calculate the perimeter of the rectangle. Quantity II: A cylinder whose radius is (1/7) of the radius of the circle and the height of the cylinder is twice the radius of the circle and the area of the circle is 154 cm2 then, find the volume of the cylinder. Correct Answer Quantity I > Quantity II

Given:

Radius of circle = 56 cm

Ratio of length and breadth of rectangle = 7 ∶ 22

Condition: The area of the circle is equal to the area of the rectangle

Concept:

Area of circle = πr2

Area of rectangle = length × breadth

Perimeter of rectangle = 2 × (length × breadth)

Calculation:

Area of circle = πr2

⇒ (22/7) × 56 × 56                 (∵ π = 22/7)

⇒ 22 × 8 × 56

⇒ 176 × 56

⇒ 9856 cm2

Now,

Let the length and breadth of the rectangle be 7x and 22x respectively.

Area of rectangle = length × breadth

⇒ 7x × 22x

⇒ 154x2

Now,

According to given Condition

⇒ 9856 = 154x2

⇒ x2 = 9856/154

⇒ x2 = 64

⇒ x = 8

Now,

Perimeter of rectangle = 2 × (l + b)

⇒ 2 × (7x + 22x)

⇒ 2 × (7 × 8 + 22 × 8)                (∵ x= 8)

⇒ 2 × (56 + 176)

⇒ 2 × 232

⇒ 464 cm

∴ The Perimeter of rectangle will be 464 cm

Quantity II:

Given:

Area of circle = 154 cm2

Radius of cylinder = (1/7) of radius of circle

Height of cylinder = twice the radius of circle

Concept:

Area of circle = πr2

Volume of cylinder = πr2h

Calculation:

Area of circle = πr2

⇒ (22/7) × r2 = 154                  (∵ π = 22/7)

⇒ r2 = 7 × 7

⇒ r2 = 49

⇒ r = 7 cm

Now,

Radius of cylinder = (1/7) × 7                       (∵ radius of circle = 7 cm)

⇒ 1 cm

Height of cylinder = 2 × 7                           (∵ radius of circle = 7 cm)

⇒ 14 cm

Now,

Volume of cylinder = πr2h

⇒ (22/7) × 1 × 1 × 14                        (∵ radius of cylinder = 1 cm, height of cylinder = 14 cm)

⇒ 22 × 1 × 1 × 2

⇒ 44 cm3

∴ The Volume of cylinder is 44 cm3

Comparison of both the result:

∴ Quantity I > Quantity II

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