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 = πr^{2}

= 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 = πr^{2}

= 22/7 × 2135 ⊂ 2135m^{2}

= 14.325850 m^{2} = 14.326m^{2 }

The area of the shot put circle = 14.326m^{2}

** **

**3. A sprinkler placed at the centre of
a flower garden sprays water covering a circular area. If the area watered is 1386
cm^{2}, find its radius and diameter.**

The area watered = 1386 cm^{2}

Area of the circle = πr^{2}

πr^{2 }= 1336

22/7 r^{2} = 1386

r^{2} = 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 = πr^{2}

= 22/7 × 56 ⊂ 56 m^{2}

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 = πr^{2}

= 22/7 × 4.9 ⊂ 4.9 m^{2}

= 75.46 m^{2}

The maximum area that the sheep can graze = **75.46 m ^{2}**

** **

**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 m^{2}.**

The area grazed by a bull πr^{2 }= 2464 m^{2}

22/7 × r^{2} = 2464 m^{2}

r^{2 }= 2464/22 ⊂ 7 = 112 × 7

r^{2 }= 784 = 28^{2}

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 = πr^{2}

= 22/7 × 63 ⊂ 63cm^{2 }

= 12474 cm^{2}

The area that will be covered by the Carpet = **12474 cm ^{2}.**

** **

**8.
Thenmozhi wants to level her circular flower garden whose diameter is 49 m
at the rate of ₹150 per m^{2}. Find the cost of levelling.**

Diameter of the flower garden d = 49 m

Radius r = 49/2 m

Area = πr^{2}

= 22/7 × 49/2 ⊂ 49/2

Area = 3773 / 2 m^{2} =1886.5 m^{2}

The cost of levelling 1 m^{2} = ₹ 150

The cost of levelling 1886.5 m^{2} = ₹ 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 m^{2}. Find the total cost of cementing the
floor.**

The radius ofthe swimming pool r = 7 m

Area = πr^{2}

= 22/7 × 7 m^{2}

Area = 154 m^{2 }

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 *r*^{2}

(ii) π *r*^{2}

(iii) 2 π *r*^{2}

(iv)
*r** *^{2}* *+*
*2*r*

** Answer :** (ii) πr

**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}*

(ii) π *m*^{2} *sq. units*

(iii) π *r*^{2} *sq. units*

(iv) π n^{2} *sq. units*

** Answer :** (iv) πn

* *

__ANSWERS:__

**Exercise 2.2**

1. 8662.5 *cm*^{2}

2. 3.581*m*^{2}

3. *r* = 21 *cm*; *d*=42 *cm*

4. 9856 *m*^{2}

5. 75.46 *m*^{2}

6. *r* = 28* m *

7. 12474 *cm*^{2}

8. ₹282975

9. ₹2772

**Objective type questions **

10. (ii) π r^{2}

11. (i) 2:1

12. (iv) π *n*^{2}

^{}

Tags : Questions with Answers, Solution | Measurements | Term 2 Chapter 2 | 7th Maths , 7th Maths : Term 2 Unit 2 : Measurements

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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

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