NCERT Class 7 Maths Chapter 11 Perimeter and Area Exercise 11.3

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 cm
Answer:

Circumference of a circle = 2πr
                  = 2 x 22/7 x 14
                  = 22/7 x 28
                  = 88 cm
(b) 28 mm
Answer:

Circumference of a circle = 2πr
                  = 2 x 22/7 x 28
                  = 22/7 x 56
                  = 176 mm
(c) 21 cm
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
               = 22/7 x 14²
               = 22/7 x 196
               = 616 mm²

(b) Diameter = 49 m
Answer:
Radius = Diameter/2
    = 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
               = 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
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
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)
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
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/m². (Take π = 3.14)
Answer:
Circular table top diameter = 1.6 m (160 cm)
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
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 = ?
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
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:

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:

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:

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
                    = 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
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
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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