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Doctors Medicines MCQs Q&A

  1. Quantity I > Quantity II
  2. Quantity I ≥ Quantity II 
  3. Quantity II > Quantity I
  4. Quantity II ≥ Quantity I
  5. Quantity I = Quantity II or Relation cannot be established
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1 Answers

Option 1 : 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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