Question

The total area of a circle and a square is equal to 2611 sq. cm. The diameter of the circle is 42 cm. What is the sum of the circumference of the circle and the perimeter of the square?(Take π = \(\frac{22}{7}\)) 
1. 280 cm
2. 272 cm
3. 380 cm
4. Cannot be determined

Answer 1

Correct Answer - Option 2 : 272 cm

Given:

The total area of a circle and a square = 2611 cm² 

The diameter of the circle = 42 cm

Formula used:

If the diameter of a circle is d, then the area of a circle = (π/4) × d² 

and circumference of a circle = π × d

If the side of a square = a, then an area of a square = a²

and perimeter = 4 × a

Calculation:

The total area of a circle and a square = 2611 cm2 

⇒ (π/4) × d2 + a2 = 2611

⇒ (22/7)× (1/4) × 42² + a² = 2611

⇒ (38808/28) + a² = 2611

⇒ 1386 + a² = 2611

⇒ a² = 2611 - 1386

⇒ a² = 1225

⇒ a = 35 cm

Now, the sum of the circumference of the circle and the perimeter of the square =  perimeter of a square + circumference of a circle

⇒ 4 × 35 + π × 42

⇒ 140 + (22/7) × 42

⇒ 140 + 132

⇒ 272 cm

∴ The sum of the circumference of the circle and the perimeter of the square is 272 cm.