The total area of a circle and a square is equal to 2611 sq. cm. The d

1.	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 cm2. 272 cm3. 380 cm4. Cannot be determined
Answer» 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.

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 cm2. 272 cm3. 380 cm4. Cannot be determined

Answer» 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.