Question

(b)Find the area of the circle, whose

circumference is 17.6m. ​

Answer 1

Given :-

Circumference of the circle = 17.6m

To find :-

Area of the circle

Formulas used :-

Area of a circle = πr² (r denoting radius)

Circumference of a circle = 2πr (or) πd (d denoting diameter, as diameter is 2 times radius)

Let us assume radius to be r.

Accordingly,

Circumference of the circle = 2 × π × r

$17.6 = 2\pi \times r$

Transposing 2 to the LHS (Left Hand Side),

$\dfrac{17.6}{2} = \pi \: \times r$

$8.8 = \pi \times r$

Substituting the value of π as 22/7,

$8.8 = \dfrac{22}{7} \times r$

Transposing 22/7 to the LHS (Left Hand Side),

$8.8 \div \dfrac{22}{7} = r$

Reciprocating 22/7 as it's divison,

$8.8 \times \dfrac{7}{22} = r$

$\cfrac{8.8 \times 7}{22} = r$

$\dfrac{61.6}{22} = r$

$2.8 = r$

Now that we know the value of radius, let us apply the formula to find the area :-

$area = \pi \times (2.8)^{2}$

Substituting the value of π as 22/7,

$area = \dfrac{22}{7} \times 2.8 \times 2.8$

By reducing to the lowest terms,

$area = 24.64m^{2}$

Area = 24.64m²

formulas :-

Area of circle = πr²

Circumference/Perimeter of circle = 2πr or πd

[d denotes diameter and r denotes radius]