Question

findthe area of the circles with :
i radius = 4.2 m
(ii) radius = 126 m (iii) radius = 63 dm
diameter = 42 m (v) circumference = 132 m (vi) circumference = 66 cm​

Answer 1

QUESTION :

Find the area of the circles with :

(i) radius = 4.2 m

(ii) radius = 126 m

(iii) radius = 63 dm

(iv) diameter = 42 m

(v) circumference = 132 m

(vi) circumference = 66 cm

SOLUTION :

(i) radius = 4.2 m

⟹ We have to find area of circle with the given radius 4.2 m

Now to find area with given radius we will use the formula :-

$A = \pi {r}^{2}$

where :-

• A = area of circle
• r = radius of circle

Now put given radius 4.2 in the formula to get answer :-

⟹$A = \frac{22}{7} \times {(4.2)}^{2}$

⟹$A = \frac{22}{7} \times 4.2 \times 4.2$

⟹$A = \frac{22}{7} \times \frac{42}{10} \times \frac{42}{10}$

⟹$A = \frac{22}{1} \times \frac{6}{10} \times \frac{42}{10}$

⟹$A = \frac{22 \times 6 \times 42}{1 \times 10 \times 10}$

⟹$A = \frac{5544}{100}$

⟹$A = 55.44 {m}^{2}$

(ii) radius = 126 m

⟹ We have to find area of circle with the given radius 126 m

Now to find area with given radius we will use the formula :-

$A = \pi {r}^{2}$

where :-

A = area of circle

r = radius of circle

Now put given radius 126 in the formula to get answer :-

⟹$A = \frac{22}{7} \times {(126)}^{2}$

⟹$A = \frac{22}{7} \times 126 \times 126$

⟹$A = \frac{22}{1} \times 18 \times 126$

⟹$A = 49896 {m}^{2}$

(iii) radius = 63 dm

⟹ We have to find area of circle with the given radius 63 dm

Now to find area with given radius we will use the formula :-

$A = \pi {r}^{2}$

where :-

A = area of circle

r = radius of circle

Now put given radius 63dm in the formula to get answer :-

⟹$A = \frac{22}{7} \times {(63)}^{2}$

⟹$A = \frac{22}{7} \times 63 \times 63$

⟹$A = \frac{22}{1} \times 9 \times 63$

⟹$A = 12474 {dm}^{2}$

iv) diameter = 42 m

⟹ We have to find area of circle with the given diameter 42m

Now to find area with given diameter we will use the formula :-

$A = \pi {d/2}^{2}$

where :-

A = area of circle

d = diameter of circle

Also , we know diameter =2× radius

Therefore we will find out radius with given diameter:-

42 = 2r ( r= radius)

42/2= r

21 metres = r

⟹$A = \frac{22}{7} \times {(21)}^{2}$

⟹$A = \frac{22}{7} \times 21 \times 21$

⟹$A = \frac{22}{1} \times 3 \times 21$

⟹$A = 1386 {m}^{2}$

(v) circumference = 132 m

circumference = 2πr

where : r = radius of circle

⟹132 = 2πr

⟹132/2= πr

⟹66= 22/7 r

⟹(66×7)/22= r

⟹3×7= r

⟹21=r

Now to find area with given radius we will use the formula :-

$A = \pi {r}^{2}$

where :-

A = area of circle

r = radius of circle

Now put given radius 21 in the formula to get answer :-

⟹$A = \frac{22}{7} \times {(21)}^{2}$

⟹$A = \frac{22}{7} \times 21 \times 21$

⟹$A = \frac{22}{1} \times 3 \times 21$

⟹$A = 1386 {m}^{2}$

(vi) circumference = 66 cm

circumference = 2πr

circumference = 2πrwhere : r = radius of circle

⟹66 = 2πr

⟹66/2= πr

⟹33= 22/7 r

⟹(33×7)/22= r

⟹(3×7)/2= r

⟹21/2 =r

Now to find area with given radius we will use the formula :-

$A = \pi {r}^{2}$

where :-

A = area of circle

r = radius of circle

⟹$A = \frac{22}{7} \times {(21/2)}^{2}$

⟹$A = \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}</p><p>⟹[tex]A = \frac{11}{1} \times \frac{3}{1} \times \frac{21}{2}</p><p>⟹[tex]A = \frac{693}{2} {cm}^{2}$

ANSWER :

i. $A = 55.44 {m}^{2}$

ii. $A = 49896 {m}^{2}$

iii. $A = 12474 {dm}^{2}$

iv. $A = 1386 {dm}^{2}$

v. $A = 1386 {m}^{2}$

vi. $A = \frac{693}{2} {cm}^{2}$

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LEARN MORE:-

1. Area of triangle = 1/2 × base× height

2. Area of rectangle = length × breadth

3. Area of square = (side)²

4. Area of Rhombus = 1/2× diagonal 1 × diagonal 2

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