Exercise 2.2 (Area of the Circle)

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 r^p sq. units

(ii) π m² sq. units

(iii) π r² sq. units

(iv)  π n² sq. units

Answer : (iv) πn² sq.units

ANSWERS:

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