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# Exercise 2.3 (Area of Pathways)

7th Maths : Term 2 Unit 2 : Measurements : Area of Pathways : Text Book Back Exercises Questions with Answers, Solution

Exercise 2.3

1. Find the area of a circular pathway whose outer radius is 32 cm and inner radius is 18 cm.

Outer radius R = 32 cm

Inner radius r = 18 cm

Area of the circular pathway = π (R2 – r2)

= 22/7 (322–182) cm2

= 22/7 (32 +18)(32 –18) cm2

= 22/7 × 50 × 14 cm2

= 2200 cm2

Area of the Circular pathway = 2200 cm2.

2. There is a circular lawn of radius 28 m. A path of 7 m width is laid around the lawn. What will be the area of the path?

Inner radius of the circle r = 28 m

Width of the path w = 7m

Outer radius of the circle R = r + w

= 28 + 7 = 35 m

Area of the pathway = π (R2 – r2)

= π (R+ r)(R+ r)

= 22/7 (35 + 28)(35 – 28) m2

= 22/7 × 63 7m2

= 1386 m2

Area of the pathway = 1386 m2.

3. A circular carpet whose radius is 106 cm is laid on a circular hall of radius 120 cm. Find the area of the hall uncovered by the carpet.

Radius of the circular Hall R = 120 cm

Radius of the circular carpet r = 106 cm

The area of the hall uncovered by the carpet = πR2 – πr2

= π (R2 – r2)

= π (R+ r)(R – r)

= 22/7 (120 +106)(120 –106) cm2

= 22/7 × 226 × 14 cm2

= 9944 cm2

The area of the hall uncovered by the Carpet = 9944 cm2.

4. A school ground is in the shape of a circle with radius 103 m. Four tracks each of 3 m wide has to be constructed inside the ground for the purpose of track events. Find the cost of constructing the track at the rate of ₹50 per sq.m. Outer radius of the circular ground R = 103 m

Width of the track w = 3m

Inner radius of the ground r = R – w

= (103 –3) m = 100 m

Area of the track = π (R2 – r2)

= 22/7 (1032 – 1002) m2

= 22/7 (10609 – 10000) m2

= 22/7 × 609 = 1914 m2

Area of the track = 1914 m2

The cost of constructing the track for 1 sq.m = ₹ 50

The cost of constructiog 1914 squ.m = ₹ 1914 × 50

= ₹ 95700

The cost of constructing the track = ₹ 95700.

5. The figure shown is the aerial view of the pathway.Find the area of the pathway. Area of the outer rectangle = 80 × 50 m2

= 4000 m2

Area of the inner rectangle = 70 × 40 = 2800 m2

The area of the pathway = Area of the outer rectangle – Area of the inner rectangle.

= 4000m2 – 2800m2 = 1200 m2

6. A rectangular garden has dimensions 11 m × 8 m. A path of 2 m wide has to be constructed along its sides. Find the area of the path.

Area of the outer rectangular garden = 11 × 8 = 88 m2

Width of the path = 2 m

Area of the inner rectangular garden = (11 – 4) (8 – 4) m2

= 7 × 4 = 28 m2

Area of the path = Outer Area – Inner Area

= (88 – 28)m2 = 60 m2

Area of the path = 60 m2.

7. A picture is painted on a ceiling of a marriage hall whose length and breadth are 18 m and 7 m respectively. There is a border of 10 cm along each of its sides. Find the area of the border.

Area of the ceiling = 18 × 7 = 126 m2

Width ofthe border  w = 10 cm = 0.1m

Inner area of the picture = (18 – 0.2) (7 – 0.2)m2

= 17.8 × 6.8 = 121.04 m2

Area ofthe border = Area ofthe Ceiling – Area ofthe Picture

= (126 – 121.04)m2 = 4.96 m2

The area of the border = 4.96 m2.

8. A canal of width 1 m is constructed all along inside the field which is 24 m long and 15 m wide. Find (i) the area of the canal (ii) the cost of constructing the canal at the rate of ₹12 per sq.m.

Outer area of the field = 24 × 15 m2 = 360 m2

Width of the Canal = 1 m

Inner area of the field = (24 – 2) (15 – 2) m2

= 22 × 13m2 = 286m2

i) Area of the canal = Outer area of the field – Inner area of the field.

= (360 – 286) m2 = 74m2

ii) The cost of constructing the canal for 1 sq.m = ₹ 12

The cost of constructing the canal for 74 m2 = ₹ 12 × 74

= ₹ 888

The cost of constructing the canal = ₹ 888

Objective type questions

9. The formula to find the area of the circular path is

(i) π(R 2 r2 ) sq. units

(ii) πr2 sq. units

(iii) 2πr2 sq. units

(iv) πr2 + 2r sq. units

Answer: (i) π (R2 – r2) sq. units

10. The formula used to find the area of the rectangular path is

(i) π(R2 r2 ) sq. units

(ii) (L × B) (l × b) sq. units

(iii) LB sq. units

(iv) lb sq. units

Answer: (ii) (L × B) – (l × b) sq. units

11. The formula to find the width of the circular path is

(i) ( L l ) units

(ii) ( B b ) units

(iii) ( R r ) units

(iv) ( r R ) units

Answer: (iii) (R – r) units

Exercise 2.3

1. 2200 cm2

2. 1386 m2

3. 9944 cm2

4. ₹95700

5. 1200 m2

6. 60 m2

7. 4.96 m2

8. (i) 74 m2 (ii) ₹888

Objective type questions

9. (i) π( R2r2 ) sq.units

10. (ii) (L × B) − (l × b) sq.units

11. (iii) R − r

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7th Maths : Term 2 Unit 2 : Measurements : Exercise 2.3 (Area of Pathways) | Questions with Answers, Solution | Measurements | Term 2 Chapter 2 | 7th Maths