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# Exercise 2.2 (Area of the Circle)

7th Maths : Term 2 Unit 2 : Measurements : Exercise 2.2 : Area of the Circle : Text Book Back Exercises Questions with Answers, Solution

Exercise 2.2

1. Find the area of the dining table whose diameter is 105 cm.

The diameter of the table d = 105 cm

Radius r = d/2 = 105/2 cm

Area = πr2

= 22/7 × 105/2 105/2 sq.cm

= 1732/2 = 8662.5 sq.cm

Area of the dining table = 8662.5 sq.cm.

2. Calculate the area of the shotput circle whose radius is 2.135 m.

The radius of the shot put circle r = 2.135 m

Area = πr2

= 22/7 × 2135 2135m2

= 14.325850 m2 = 14.326m2

The area of the shot put circle = 14.326m2

3. A sprinkler placed at the centre of a flower garden sprays water covering a circular area. If the area watered is 1386 cm2, find its radius and diameter.

The area watered = 1386 cm2

Area of the circle = πr2

πr2 = 1336

22/7 r2 = 1386

r2 = 1386/22 7 = 63 × 7

= 3 × 3 × 7 × 7 = (3 × 7)2

r = 3 × 7 = 21 cm

Radius r = 21 cm

Diameter d = 2r = 2 × 21 = 42cm

4. The circumference of a circular park is 352 m. Find the area of the park.

The circumference ofa circular park 2πr = 352 m

2 × 22/7 r = 352

r = 352 / [2 × 22] 7 = 56 m

Area = πr2

= 22/7 × 56 56 m2

Area of the park = 9856 m².

5. In a grass land, a sheep is tethered by a rope of length 4.9 m. Find the maximum area that the sheep can graze. The length of the rope a sheep tethered = 4.9 m

Radius of the circle r = 4.9m

Area = πr2

= 22/7 × 4.9 4.9 m2

= 75.46 m2

The maximum area that the sheep can graze = 75.46 m2

6. Find the length of the rope by which a bull must be tethered in order that it may be able to graze an area of 2464 m2.

The area grazed by a bull πr2 = 2464 m2

22/7 × r2 = 2464 m2

r2 = 2464/22 7 = 112 × 7

r2 = 784 = 282

r = 28 m

The length of the rope = 28m

7. Lalitha wants to buy a round carpet of radius is 63 cm for her hall. Find the area that will be covered by the carpet.

The radius of the carpet r = 63 cm

Area = πr2

= 22/7 × 63 63cm2

= 12474 cm2

The area that will be covered by the Carpet = 12474 cm2.

8. Thenmozhi wants to level her circular flower garden whose diameter is 49 m at the rate of ₹150 per m2. Find the cost of levelling.

Diameter of the flower garden d = 49 m

Radius r = 49/2 m

Area = πr2

= 22/7 × 49/2 49/2

Area = 3773 / 2   m2 =1886.5 m2

The cost of levelling 1 m2 = ₹ 150

The cost of levelling 1886.5 m2 = ₹ 1886.5 × 150

The cost of levelling the flower garden = ₹ 282975.

9. The floor of the circular swimming pool whose radius is 7 m has to be cemented at the rate of ₹18 per m2. Find the total cost of cementing the floor.

The radius ofthe swimming pool r = 7 m

Area = πr2

= 22/7 × 7 m2

Area = 154 m2

The cost of cementing 1 sq.m = ₹ 18

The cost of cementing 154 sq.m = ₹ 154 × 18

= ₹2772

The total cost of cementing the floor = ₹ 2772.

Objective type questions

10. The formula used to find the area of the circle is ______ sq.units.

(i) 4 π r2

(ii) π r2

(iii) 2 π r2

(iv) r 2 + 2r

Answer : (ii) πr2

11. The ratio of the area of a circle to the area of its semicircle is

(i) 2:1

(ii) 1:2

(iii) 4:1

(iv) 1:4

Answer : (i) 2:1

12. Area of a circle of radius ‘n’ units is

(i) 2 π rp sq. units

(ii) π m2 sq. units

(iii) π r2 sq. units

(iv)  π n2 sq. units

Answer : (iv) πn2 sq.units

Exercise 2.2

1. 8662.5 cm2

2. 3.581m2

3. r = 21 cm;  d=42 cm

4. 9856 m2

5. 75.46 m2

6. r = 28 m

7. 12474 cm2

8. ₹282975

9. ₹2772

Objective type questions

10. (ii) π r2

11. (i) 2:1

12. (iv) π n2

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7th Maths : Term 2 Unit 2 : Measurements : Exercise 2.2 (Area of the Circle) | Questions with Answers, Solution | Measurements | Term 2 Chapter 2 | 7th Maths