Copper wire of length 44cm is to be bent into a square and a circle which will have a length and breadth with full Explanation
Answers
CORRECT QUESTION:
Q: Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take π = 22/7)
Answer:
- Radius of circle = 7 cm
- Area of a circle = 154 cm²
- Length of each sides of square = 11 cm
- Area of a square = 121 cm²
- Circle encloses more area.
Step-by-step explanation:
Given that:
- Length of a wire = 44 cm
To Find:
- Radius of circle.
- Area of a circle.
- Length of each sides of square.
- Area of a square.
- Which figure encloses more area?
Formula used:
- Circumference of a circle = 2πr
- Area of a circle = πr²
- Perimeter of a square = 4a
- Area of a square = a²
Here,
- Radius of a circle is denoted as r.
- Side of a square is denoted as a.
Finding the radius of circle:
⟼ 2πr = 44
⟼ r = 44/2π
⟼ r = (44 × 7)/(2 × 22)
⟼ r = 7
Radius of circle = 7 cm
Finding the area of a circle:
- Area of circle = π(7 cm)²
- Area of circle = (22 × 7 cm × 7 cm)/7
- Area of circle = 154 cm²
Finding the length of each sides of square:
⟼ 4a = 44
⟼ a = 44/4
⟼ a = 11
Each sides of a square = 11 cm
Finding the area of a square:
- Area of square = (11 cm)²
- Area of square = (11 cm × 11 cm)
- Area of square = 121 cm²
Which figure encloses more area:
- After finding the area of circle and area of square we get that the area of circle is greater than that of square.
CORRECT QUESTION:
Q: Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take π = 22/7)
Answer:
Radius of circle = 7 cm
Area of a circle = 154 cm²
Length of each sides of square = 11 cm
Area of a square = 121 cm²
Circle encloses more area.
Step-by-step explanation:
Given that:
Length of a wire = 44 cm
To Find:
Radius of circle.
Area of a circle.
Length of each sides of square.
Area of a square.
Which figure encloses more area?
Formula used:
Circumference of a circle = 2πr
Area of a circle = πr²
Perimeter of a square = 4a
Area of a square = a²
Here,
Radius of a circle is denoted as r.
Side of a square is denoted as a.
Finding the radius of circle:
⟼ 2πr = 44
⟼ r = 44/2π
⟼ r = (44 × 7)/(2 × 22)
⟼ r = 7
Radius of circle = 7 cm
Finding the area of a circle:
Area of circle = π(7 cm)²
Area of circle = (22 × 7 cm × 7 cm)/7
Area of circle = 154 cm²
Finding the length of each sides of square:
⟼ 4a = 44
⟼ a = 44/4
⟼ a = 11
Each sides of a square = 11 cm
Finding the area of a square:
Area of square = (11 cm)²
Area of square = (11 cm × 11 cm)
Area of square = 121 cm²
Which figure encloses more area:
After finding the area of circle and area of square we get that the area of circle is greater than that of square