Perimeter and Area
Exercise 11.3
1). Find the circumference of the circles with the following radius: (Take p =22/7)
(a) 14 cm (b) 28 mm (c) 21 cm
Solution:
(a) 14 cm
Given: radius = 14 cm
Circumference = 2pr
= 2 X 22/7 X 14
= 2 X 22 X 2
= 88 cm
Ans: circumference = 88 cm
(b) 28 mm
Given: radius = 28 mm
Circumference = 2pr
= 2 X 22/7 X 28
= 2 X 22 X 4
= 196 mm
Ans: circumference = 196 mm
(c) 21 cm
Given: radius = 21 cm
Circumference = 2pr
= 2 X 22/7 X 21
= 2 X 22 X 3
= 132 cm
Ans: circumference = 132 cm
2). Find the area of the following circles, given that:
(a) radius = 14 mm (Take p =22/7)
(b) diameter = 49 m
(c) radius = 5 cm
Solution:
(a) radius = 14 mm (Take p =22/7)
Given: radius = 14 mm
Area of circle = pr2
= 22/7 X (14)2
= 22/7 X 14 X 14
= 616 sq mm
(b) diameter = 49 m
radius = diameter/2
= 49/2
Area of circle = pr2
= 22/7 X (49/2)2
= (22 X 49 X 49)/(7 X 2 X 2)
= (11 X 7 X 49)/2
= 1886.50 sq m
(c) radius = 5 cm
Area of circle = pr2
= 22/7 X (5)2
= 22/7 X 5 X 5
= 78.57 sq cm
3). If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take p =22/7)
Given: Circumference of a sheet = 154 m
To Find: radius of the sheet = ?
Area of the sheet = ?
Circumference = 2pr
54 = 2 X 22/7 X r
2 X 22/7 X r = 154
r = (154 X 7)/ (22 X 2)
r = 24.5 m
area of the sheet = pr2
= 22/7 X 24.5 X 24.5
= 22 X 3.5 X 24.5
= 1886.5 sq m
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 p = 22/7)
Given: diameter of circular garden = 21 m
rounds of fence = 2
rate of fencing = ₹ 4 per meter
To Find: length of the rope to fence = ?
1 round of fence = circumference of garden
= pd
= 22/7 X 21
= 22 X 3
= 66 m
Length of the rope = circumference X number of rounds
= 66 X 2
= 132 m
Cost of fencing = Rate X Length of the rope
= 4 X 132
=₹ 528
Ans: length of the rope = 132 m
Cost of fencing = ₹ 528
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 p = 3.14)
Given: Radius of larger circle = R = 4 cm
Radius of smaller circle = r = 3 cm
To Find: Area of remaining sheet = ?
Area of remaining sheet = pR2 – pr2
= p(R2 – r2)
= 22/7 (42 – 32)
=22/7 (16-9)
= 22/7 X 7
= 22 sq m
Ans: Area of the remaining sheet = 22 sq m.
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 cost₹ s 15. (Take p = 3.14)
Given: diameter of circular table = 1.5 m
Rate of the lace = ₹ 15
To Find: length of the lace
Length of the lace = circumference of table cover
= pd
= 3.14 X 1.5
= 4.71 m
Cost of the lace = Rate X circumference
= 15 X 4.71
= ₹ 70.65
Ans: cost of the lace = ₹ 70.65
7). Find the perimeter of the adjoining figure, which is a semicircle including its diameter.
Given: diameter of semicircle = 10 cm
To Find: perimeter of semi circle = ?
Radius = diameter / 2
= 10/2 = 5 cm
Perimeter of semi circle = ½ X circumference + diameter
= ½ X 2pr + d
= pr + d.
= 22/7 X 5 + 10
= 3.14 X 5 + 10
= 15.7 + 10
= 25.7 cm
Ans: perimeter of semicircle = 25.7 cm
8). Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is ₹ 15/m2. (Take p = 3.14)
Given: diameter of table-top = 1.6 m
rate of polishing = ₹ 15/m2
To Find: cost of polishing = ?
Radius = diameter/2
= 1.6/2 = 0.8 m
Area of table-top = pr2
= 3.14 X 0.8 X 0.8
= 2.0096
= 2.01
Cost of polishing = Rate X Area
= 15 X 2.01
= ₹ 30.15
Ans: Cost of polishing = ₹ 30.15
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 p =22/7)
Given: length of the wire = 44 cm
To find: radius of the circle = ?
area of the circle = ?
side of the square = ?
area of the square = ?
circumference of the circle = length of the wire
2pr = 44
2 X 22/7 X r = 44
r = (44 X 7)/(2 X 22)
r = 7 cm
area of the circle = pr2
= 22/7 X 7 X 7
= 22 X 7
= 154 Sq cm
Same wire is bent to shape of square
Perimeter of square = length of the wire
4 X side = 44
side = 44/4
side = 11 cm
area of square = side X side
= 11 X 11
= 121 sq cm
121 < 154
circle encloses more area
Ans: radius of the circle = 7 cm
area of the circle = 154 sq cm
side of the square = 11 cm
area of the square = 121 sq cm
circle encloses more area.
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 p =22/7)
Given: radius of card sheet = R = 14 cm
radius of smaller circle = r = 3.5 cm
length of the rectangle = 3 cm
breadth of the rectangle = 1 cm
To Find: Area of the remaining sheet
Area of the remaining sheet = Area of circular card – (area of
two circles + area of rectangle)
Area of circular card = pr2
= 22/7 X 14 X 14
= 22 X 2 X 14
= 616 sq cm
Area of small circle = pr2
= 22/7 X 3.5 X 3.5
= 22 X 0.5 X 3.5
= 11 X 3.5
= 38.5 sq cm
Area of two small circles = 2 X pr2
= 2 X 38.5
= 77 sq cm
Area of rectangle = length X breadth
= 3 X 1
= 3 sq cm
Area of the remaining sheet = Area of circular card – (area of
two circles + area of rectangle)
= 616 – ( 77 + 3)
= 616 – 80
= 536 sq cm
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 p = 3.14)
Given: radius of circle = r = 2 cm
side of square = s = 6 cm
To Find: area of left over aluminium sheet = ?
Area of circle = pr2
= 3.14 X 2 X 2
= 12.56 sq cm
Area of square = side X side
= 6 X 6
= 36 sq cm
Area of the left over sheet = area of square – area of circle
= 36 – 12.56
= 23.44 sq cm
Ans: Area of the left over sheet = 23.44 sq cm
12). The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take p = 3.14)
Given: circumference of circle = 31.4 cm
To Find: radius = ?
Area = ?
circumference = 31.4
2pr = 31.4
2 X 3.14 X r = 31.4
r = 31.4 X ½ X 1/3.14
r = (31.4 X 1)/(3.14 X 2)
r = 5 cm
r = 5 cm
Area of circle = pr2
= 3.14 X 5 X 5
= 78.5 sq cm
Ans: radius = 5 cm
Area of circle = 78.5 sq cm
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?
(p = 3.14)
Given: diameter of the flower bed = 66 m
width of the path = 4 m
To Find: area of the path = ?
Diameter of the flower bed = 66
radius of the flower bed r = Diameter/2
= 66/2
= 33 m
radius of the outer circle formed = R = 33 + 4
= 37 m
Area of remaining sheet = pR2 – pr2
= p(R2 – r2)
= 3.14 (372 – 332)
= 3.14 (1369 – 1089)
= 3.14 X 280
= 879.20 sq m
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 p = 3.14)
Given: Area of flower garden = 314 m2
Radius of area that sprinkle can cover = 12 m
Area of flower garden = 314
pr2 = 314
3.14 X r2 = 314
r2 = 314 / 3.14
r2 = 100
taking square root on both the sides
r = 10 m
since 10 < 12
sprinkler can water the entire garden
15). Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take p = 3.14)
Given: outer radius = R = 19 m
width of the road = 10 m
To Find: circumference of inner and the outer circles
radius of inner circle = outer radius – width of the road
= 19 – 10
r = 9 m
circumference of outer circle = 2pR
= 2 X 3.14 X 19
= 119.32 m
circumference of inner circle = 2pr
= 2 X 3.14 X 9
= 56.52 m
Ans: circumference of outer circle = 119.32 m
circumference of inner circle = 56.52 m
16). How many times a wheel of radius 28 cm must rotate to go 352 m? (Take p = 22/7)
Given: radius of wheel = 28 cm
distance = 352 m = 352 X 100 = 35200 cm
To Find: times the wheel rotate to cover 35200 cm
one rotation of the wheel = circumference of circle
= 2pr
= 2 X 22/7 X 28
= 2 X 22 X 4
= 176 cm
No of times wheel rotates = distatnce / circumference
= 35200 / 176
= 200
Ans: number of rotation of wheel = 200
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 p = 3.14)
Given: length of the minute hand = radius = 15 cm
Time = 1 hour
To Find = distance covered in 1 hour
Distance covered by minute hand = circumference
= 2pr
= 2 X 3.14 X 15
= 94.2 cm
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