Question

If a circle and a square have the same area, then what will be the perimeter of the square, if the diameter of the circle is 8 cm.

• A. 8√𝝅
• B. 16/π
• C. 16√𝝅
• D. 8π

Answer 1

Answer:

C. 16√𝝅

Mathematics - Mensuration (2D Shapes)

• Problem Analysis: This problem involves comparing a circle and a square with equal areas and finding the perimeter of the square given the circle's diameter.

• Key Concepts:

  • Area of a circle: A = πr², where 'r' is the radius.

  • Area of a square: A = s², where 's' is the side length.

  • Perimeter of a square: P = 4s.

• Given Information:

  • Diameter of the circle = 8 cm.

  • Area of the circle = Area of the square.

• Step-by-Step Solution:

  1. Calculate the radius of the circle: Radius (r) = Diameter / 2 = 8 cm / 2 = 4 cm.

  2. Calculate the area of the circle: Area = π * (4 cm)² = 16π sq cm.

  3. Equate areas: Since the area of the square is equal to the area of the circle, the area of the square is also 16π sq cm.

  4. Find the side length of the square: Area of square = s² = 16π sq cm. Therefore, s = √(16π) cm = 4√π cm.

  5. Calculate the perimeter of the square: Perimeter = 4 * s = 4 * (4√π cm) = 16√π cm.