## Chapter 11 Perimeter and Area Exercise 11.3

**Question 1: Find the circumference of the circle with the following radius: (Take π = 22/7)(a) 14 cmAnswer:**

Circumference of a circle = 2πr

= 2 x 22/7 x 14

= 22/7 x 28

= 88 cm

**(b) 28 mm**

Answer:

Answer:

Circumference of a circle = 2πr

= 2 x 22/7 x 28

= 22/7 x 56

= 176 mm

**(c) 21 cm**

Answer:

Answer:

Circumference of a circle = 2πr

= 2 x 22/7 x 21

= 22/7 x 42

= 132 cm

**Question 2: Find the area of the following circles, given that:**

(a) Radius = 14 mm (Take π = 22/7)

Answer:

Area of circle = πr²

(a) Radius = 14 mm (Take π = 22/7)

Answer:

= 22/7 x 14²

= 22/7 x 196

= 616 mm²

**(b) Diameter = 49 m**

Answer:

Radius = Diameter/2

Answer:

= 49/2

= 24.5 m

Area of circle = πr²

= 22/7 x 24.5²

= 22/7 x 600.25

= 1886.5 m²

**(c) Radius = 5 cm**

Answer:

Area of circle = πr²

Answer:

= 22/7 x 5²

= 22/7 x 25

= 78 4/7 cm²

**Question 3: If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take π = 22/7)**

Answer:

Circumference of a circular sheet = 154 m

Answer:

Perimeter of a circle = 2πr

= 2 x 22/7 x r = 154

= 44r/7 = 154

= 44r = 154 x 7

r = 154 x 7/44 = 49/2 m

= 49/2 m

Therefore, the radius is 49/2 m.

Area of circle = πr²

= 22/7 x 49/2 x 49/2

= 52822/28

= 1886.5 m²

Therefore, the area of circular sheet is 1886.5 m².

**Question 4: A gardener wants to fence a circular garden of diameter 21m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs ₹ 4 per meter. (Take π = 22/7).**

**Answer:**

Diameter = 21 m

Circumference = ?

Radius = Diameter/2

= 21/2

= 10.5 m

Therefore, the radius of circular garden is 10.5 m.

Circumference = 2πr

= 2 x 22/7 x 10.5

= 22/7 x 21

= 66 m

Therefore, the circumference of the circle is 66 m.

Rope required to fence the garden = ?

Circumference of the circular garden = 66 m

Rounds required = 2

= 66 x 2 = 132 m

Therefore, the rope required is 132 m.

Cost of rope = ?

Cost of rope (per meter) = ₹ 4

Rope required = 132 m

= 132 x 4 = ₹ 528

Therefore, the cost of rope required is ₹ 528.

**Question 5: From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take π = 3.14)**

Answer:

Circular sheet radius = 4 cm

Answer:

Area = ?

Area of circle = πr²

= 3.14 x 4 x 4

= 50.24 cm²

Small circle radius = 3 cm

Area = ?

Area of circle = πr²

= 3.14 x 3 x 3

= 28.26 cm²

The area of remaining sheet = ?

= 50.24 cm² - 28.26 cm²

= 21.98 cm²

Therefore, the area of remaining sheet is 21.98 cm².

**Question 6: Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15. (Take π = 3.14)**

Answer:

The diameter of circular table = 1.5 m (150 cm)

Answer:

Radius = ?

Radius = Diameter /2

= 150/2

= 75 cm

Therefore, the radius of the circular table is 75 cm.

Length of lace required = ?

Circumference = 2πr

= 2 x 3.14 x 75

= 471 cm (4.71 m)

Cost of lace required = ?

Cost of 1 m lace = ₹ 15

Length of lace (in meters) = 4.71 m

= 15 x 4.71

= ₹ 70.65

Therefore, the cost of lace required is ₹ 70.65.

**Question 7: Find the perimeter of the adjoining figure, which is a semicircle including its diameter.**

Answer:

Diameter = 10 cm

Answer:

Radius = Diameter/2

= 10/2

= 5 cm

Therefore, the radius is 5 cm.

Perimeter of given figure = ?

= curved part + diameter

= πr + d

= 3.14 x 5 + 10

= 15.70 + 10

= 25.70 cm

Therefore, the perimeter of the given figure is 25.70 cm.

**Question 8: Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is ₹ 15/m**

**². (Take π = 3.14)**

Answer:

Circular table top diameter = 1.6 m (160 cm)

Answer:

Radius = ?

Radius = Diameter/2

= 160/2

= 80 cm (0.8 m)

Therefore, the radius of circular table top is 80 cm or 0.8 m.

Area of circle = πr²

= 3.14 x 0.8 x 0.8

= 2.0096 m²

Therefore, the area of table top is 2.0096 m².

Cost of polishing it = ?

Cost of polishing 1 m² = ₹ 15

= 2.0096 x 15

= ₹ 30.144

= ₹ 30.14 (approximately)

Therefore, the cost of polishing table top is ₹ 30.14 (approximately).

**Question 9: Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take π = 22/7)**

Answer:

Wire length = 44 cm

Answer:

Circumference of circle = 2πr

44 = 44/7 x r

= 44 x 7/44 = r

= 308/44 = 7 cm

Therefore, the radius is 7 cm.

Area of circle = πr²

= 22/7 x 7 x 7

= 1078/7

= 154 cm²

Therefore, the area of the circle is 154 cm².

Perimeter of square = 4 x side

44 = x/4

= 44/4

= 11 cm

Therefore, the length of each side of square is 11 cm.

Area of square = side x side

= 11 x 11

= 121 cm²

Therefore, the area of square is 121 cm².

Compare

154 cm² > 121 cm²

Therefore, the circle encloses more area.

**Question 10: From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1cm are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (Take π = 22/7)**

Answer:

Area of circular sheet = ?

Answer:

Radius = 14 cm

Area of circle = πr²

= 22/7 x 14 x 14

= 22/7 x 196

= 4312/7

= 616 cm²

Therefore, the area of circular sheet is 616 cm².

The area of small circle = ?

Radius = 3.5 cm

Area of circle = πr²

= 22/7 x 3.5 x 3.5

= 22/7 x 12.25

= 269.5/7

= 38.5 cm²

Therefore, the area of circle is 38.5 cm².

38.5 x 2 = 77 cm²

Therefore, the area of 2 small circles is 77 cm².

Length of rectangle = 3 cm

Breadth of rectangle = 1 cm

Area = length x breadth

= 3 x 1

= 3 cm²

Therefore, the area of rectangle is 3 cm².

= 616 cm² - (77 cm² + 3 cm²)

= 616 cm² - 80 cm² = 536 cm²

Therefore, the area of remaining sheet is 536 cm².

**Question 11: A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side**

6 cm. What is the area of the left over aluminium sheet? (Take π = 3.14)

Answer:

Given

6 cm. What is the area of the left over aluminium sheet? (Take π = 3.14)

Answer:

Square side = 6 cm

Area of the square = side x side

= 6 x 6

= 36 cm²

Circle radius = 2 cm

Pi value = 3.14

Area of circle = πr²

= 3.14 x 2 x 2

= 3.14 x 4

= 12.56 cm²

The area of the leftover sheet = Area of square - Area of circle

= 36 - 12.56

= 23.44 cm²

Therefore, the area of leftover sheet is 23.44 cm².

**Question 12: The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take π = 3.14)**

Answer:

Answer:

Given

Circumference of circle = 31.4 cm

Perimeter of circle = 2πr

31.4 = 2 x 3.14 x r

31.4 = 6.28r

r = 31.4/6.28

r = 5 cm

Area of circle = πr²

= 3.14 x 5 x 5

= 3.14 x 25

= 78.5 cm²

Therefore, the area of the circle is 78.5 cm².

**Question 13: A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)**

Answer:

Answer:

Given

Flower bed diameter = 66 m

Radius = Diameter/2

= 66/2

= 33 m

Therefore, the radius of flower bed is 33 m.

Outer circle = 4 + 66 + 4

= 74 m

Radius = Diameter/2

= 74/2

= 37 m

Therefore, the radius of outer circle is 37 m.

Area of flower bed = ?

Area of circle = πr²

= 3.14 x 33 x 33

= 3.14 x 1089

= 3419.49 m²

Therefore, the area of flower bed is 3419.49 m².

Area of outer circle = ?

Area of circle = πr²

= 3.14 x 37 x 37

= 3.14 x 1369

= 4298.66 m²

Therefore, the area of outer circle is 4298.66 m².

Area of path = Area of outer circle - Area of flower bed

= 4298.66 m² - 3419.49 m²

= 879.17 m²

Therefore, the area of the path is 879.17 m².

**Question 14: A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)**

Answer:

Answer:

Given

Area of circular flower garden = 314 m²

Sprinkler can cover an area of circle radius 12 m

Therefore, the area covered by sprinkler

= πr²

= 3.14 x 12 x 12

= 3.14 x 144

= 452.16 m²

Compare

= 314 m² < 452 m²

Therefore, the sprinkler can cover the entire garden.

**Question 15: Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)**

Answer:

Radius of inner circle = outer circle - 10

Answer:

= 19 - 10

= 9 m

Circumference of inner circle = 2πr

= 2 x 3.14 x 9

= 56.52 m²

Radius of outer circle = 19 m

Circumference of outer circle = 2 x 3.14 x 19

= 119.32 m²

Therefore, the perimeter of inner circle is 56.52 m² while the perimeter of outer circle is 119.32 m².

**Question 16: How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = 22/7)**

Answer:

Radius of wheel = 28 m

Answer:

Circumference of the wheel = 2πr

= 2 x 22/7 x 28

= 176 cm

= Total distance to be covered/Circumference of the wheel

= 352 m/176 cm

= 35200 cm/176 cm

= 200 times

Therefore, 200 times a wheel can cover.

**Question 17: The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take π = 3.14)**

Answer:

Length of minute hand = 15 cm

Answer:

Length of minute hand covers the distance = 1 hour

Circumference of circle = 2πr

= 2 x 3.14 x 15

= 94.2 cm

Therefore, the minute hand can cover the distance of 94.2 cm in an hour.

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