Question

1. Find
Find the radius and area of a circle, whose
th
circumference is :
Oy 132 cm
(ii) 22 m​

Answer 1

Answer:

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Answer 2

Required Solution:

To find: Radius and area of the circle whose circumference is given.

• Circumference = 132 cm

We know that,

→ Circumference of the circle = 2πr

→ 132 = 2 × $\dfrac{22}{7}$ × r

→ 132 = $\dfrac{44}{7}$ r

→ r = $\cancel{132} \times \dfrac{7}{\cancel{44}}$

→ r = 3 × 7

→ $\boxed {\sf \gray { Radius = 21cm} }$

Now, area:–

We know that,

• Area of the circle = πr²

→ Area of the circle = $\dfrac{22}{7}$ × (21)²

→ Area of the circle = $\dfrac{22}{\cancel{7}} \times \cancel{441}$

→ Area of the circle = 22 × 63

→ $\boxed {\sf \gray { Area~ of~ the~ circle = 1386 ~ {cm}^{2} } }$

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• Circumference = 22m

We know that,

• → Circumference of the circle = 2πr

→ 22 = 2 × $\dfrac{22}{7}$ × r

→ 22 = $\dfrac{44}{7}$ r

→ r = $\cancel{22} \times \dfrac{7}{\cancel{44}}$

→ r = 1 × $\dfrac{7}{2}$

→ $\boxed {\sf \gray { Radius = 3.5m} }$

Now, area:–

We know that,

• Area of the circle = πr²

→ Area of the circle = $\dfrac{22}{7}$ × (3.5)²

→ Area of the circle = $\dfrac{22}{7} \times 12.25$

→ Area of the circle = $\dfrac{269.5}{7}$

→ $\boxed {\sf \gray { Area~ of~ the~ circle = 38.5 ~ {m}^{2} } }$

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Extra!!

More areas and perimeters:–

Perimeter:

• Perimeter of square : 4 × side
• Perimeter of rectangle : 2 ( l + b )
• Perimeter of parallelogram : 2 ( l + b )
• Perimeter of rhombus : 4 × side
• Perimeter of trapezium : Sum of sides
• Perimeter of triangle : Sum of sides
• Perimeter of circle (circumference) : 2πr

Area:

• Area of square : (Side)²
• Area of rectangle : l × b
• Area of parallelogram : Base × height
• Area of rhombus : ½ × diagonal$\sf {_1}$ × diagonal$\sf {_2}$
• Area of trapezium : ½ × (sum of parallel sides) × h
• Area of triangle : ½bh
• Area of circle : πr²

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