A wire of length 44cm is bent into a circle and square:
(a) What is the side of the square .
(b) Find the radius of the circle.
(c) Find the area of the circle.
(d) Find the area of square.
(e) Compare the area of circle and square . Which is greater.
Answers
Given :
A wire of length 44cm is bent into a circle and square
To find :
(a) What is the side of the square .
(b) Find the radius of the circle.
(c) Find the area of the circle.
(d) Find the area of square.
(e) Compare the area of circle and square . Which is greater.
Formula used :
- Perimeter of square = 4 × side
- Area of square = (side)²
- Circumference of circle = 2π(radius)
- Area of circle = π (radius)²
Solution :
When wire is bent into circle or square, the length of wire will be equal to perimeter of figure formed
(a) Perimeter of square = length of wire
➝ 4 × side of square = 44cm
➝ side of square = 44cm ÷ 4
➝ side of square = 11 cm
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(b) Circumference of circle = length of wire
➝ 2×π × radius of circle = 44cm
➝ radius of circle = 44cm ÷ (2π)
➝ radius of circle = 22cm ÷ π
➝ radius of circle = 22cm × 7/22
➝ radius of circle = 7cm
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(c) Area of circle = π× (radius of circle)²
➝ Area of circle = π × (7 cm)²
➝ Area of circle = (22/7) × 49 cm²
➝ Area of circle = 22 × 7 cm²
➝ Area of circle = 154 cm²
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(d) Area of square = (side of square)²
➝ Area of square = (11 cm)²
➝ Area of square = 121 cm²
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(e)
- Area of circle = 154cm²
- Area of square = 121cm²
From above it is clear that area of circle is larger than area of square
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ANSWER :
(a) Side of the square = 11 cm
(b) Radius of the circle = 7cm
(c) Area of the circle = 154 cm²
(d) Area of square = 121 cm²
(e) Area of circle is greater