NCERT Solutions for class 7 maths Chapetr- 11 Perimeter and area Exercise-11.3
Q-1 Find the circumference of the circle with the following radius:
- 14 cm
Circumference of the circle =2∏r
=2 x (22 /7 ) x 14
= 2 x 22 x 2
= 88 cm
- 28 cm
Circumference of the circle= 2∏r
=2 x (22/7) x 28
=176 cm
- 21 cm
Circumference of the circle =2∏r
=2 x (22 / 7) x 21
= 2 x 22 x 3
= 132cm
Q-2 find the area of the following circles,given that :
- Radius=14mm
Area of the circle =∏r2
= 22/7 x 14 2
= 22/ 7 x 196
= 22 x 28
= 616 mm2
- Diameter =49m
= 49/2
= 24.5m
Area of the circle=∏r2
= 22/7 x ( 24.5 )2
= 22/7 x 600.25
= 22 x 85.75
= 1886.5 m2
- Radius =5 cm
Area of the circle =∏r2
=22/7 x 52
=22/7 x 25
=550/7
=78.57 cm2
Q-3 if the circumference of a circular sheet is 154 m , find circular sheet is 154 m, find its radius .also find the area of the sheet .
Circumference of the circle =154m
Circumference of the circle =2∏r
154=2 x (22/7) x r
154= 44/7 x r
R= (154 x 7 ) / 44
R=(14 x 7 ) / 4
R=(7 x 4 ) / 2
R= 49/2
R= 24.5 m
Area of the circle =∏r2
=22/7 x (24.5)2
=22/7 x 600.25
=22 x 85.75
=1886.5 m 2
Q-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 Rs.4 per meter.
Solution:-
Diameter of the circular garden =21m
=21/2
=10.5m
Circumference of the circle= 2∏r
=2 x (22/7) x 10.5
=462/7
=66m
Cost of 1m rope= Rs.4
Cost of 132m rope= Rs.4 x 132 = Rs.528
Q-5 from a circular sheet of radius 4cm ,a circle of radius 3 cm is removed . find the area of the remaining sheet .
Solution:-
Radius of circular sheet R =4 cm
A circle of radius to be removed r = 3 cm
=∏(R2-r2)
=3.14( 42-32)
=3.14 (16 – 9 )
=3.14 x 7
=21.98 cm2
Q-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 Rs.15 .
Solution:-
Diameter of the circular table = 1.5 m
=1.5 / 2
= 0.75 m
Circumference of the circle =2∏r
= 2 x 3.14 x 0.75
= 4.71 m
Cost of 1 m lace = Rs.15
Cost of 4.71 m lace = Rs. 15 x 4.71 = Rs.70.65
Q-7 Find the perimeter of the adjoining figure, which is a semicircle including its diameter.
Solution:-
Radius = 10/2
=5 cm
Circumference of the semi-circle =∏r
=(22/7) x 5
=110/7
=15.71 + 10
= 25.71 cm
Q-8 find the cost of polishing a circular table -top of diameter 1.6m,if the rate of polishing is Rs.15/m2.
Solution:-
Radius =1.6 m
= 1.6/2
=0.8 m
Area of the circular table – top = ∏r2
=3.14 x 0.8 2
=3.14 x 0.8 x 0.8
= 2.0096 m2
Cost for polishing 1m2 area= Rs.15
Cost for polishing 2.0096m2 area = Rs.15 x 2.0096
= Rs.30.144
Q-9 Shazil took a wire of length 44cm 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 shapes of a square ,what will be the length of each of its sides? Which figure encloses more area , the circle or the square ?
Solution:-
Circumference of the circle = 2 ∏r
44 = 2 x (22/7) x r
44 = 44/7 x r
(44 x 7)/ 44 =r
R=7cm
Area of the circle = ∏r2
=22/7 x 72
= 22/7 x 7 x 7
= 22 x 7
= 154 cm2
The length of the each side of square = 44/4
= 11cm
= 112
=121cm2
Q-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 1 cm are removed .find the area of the remaining sheet.
Solution-
Radius of the circular card sheet = 14cm
Radius of the two small circle =3.5 cm
Length of the rectangle =3cm
Breadth of the rectangle =1cm
Area of the circular card sheet =∏r2
=22/7 x 14 2
= 22/7 x 14 x 14
=22 x 2 x 14
=616 cm2
Area of the 2 small circles = 2 x ∏r
=2 x (22/7 x 3.52)
=2 x (22/7 x 12.25)
=2 x 38.5
=77cm2
=3 x 1
=3cm2
=616-(77+3)
=616-80
=536 cm 2
Also Read :- Explanation of NOUN Types / ENGLISH GRAMMAR
Q-11 a circle of radius 2cm is cut out from a square piece of an aluminium sheet of side .6cm what is the area of the left over aluminium sheet ?
Solution:-
Radius of circle= 2cm
Square sheet sides= 6cm
Area of the square= side2
=62
=36cm2
= 3.14 x 22
= 3.14 x 4
= 12.56 cm2
= 36 – 12.56
= 23.44 cm2
Q-12 the circumference of a circle is 31.4 cm. Find the radius and the area of the circle ?
Solution:-
Circumference of a circle =2∏r
31.4 =2 x 3.14 x r
31.4 =6.28 x r
31.4/6.28 = r
R = 5cm
Area of the circle = ∏r2
= 3.14 x 5 2
= 3.14 x 25
= 78.5 cm
Q-13 a circular flowers bed is surrounded by a path 4m wide.the diameter of the flower bed is 66 m. what is the area of this path ?
Solution:-
Radius of the flower bed = d/2
=66/2
=33m
Area of flower bed =∏r2
=3.14 x 33 2
=3.14 x 1089
=3419.46 m
Area of the flower bed and path together= ∏r2
=3.14 x 372
=3.14 x 1369
=4298.66 m
Area of the path = area of the flower bed and path together – area of flower bed
=4298.66 – 3419.46
=879.20 m2
Q-14 A circular flower garden has an area of 314 m2.a splinker at the centre of the garden can cover an area that has a radius
of 12m .will the sprinkler water the entire garden ?
Solution:-
Area of the circular flower garden = ∏r2
314 = 3.14 x r2
314/3.14 = r2
R2 = 100
R = √100
R = 10m
Q15. Find the circumference of the inner and the outer circles shown in the adjoining figure ?
Solution:-
Radius of inner circle = outer circle radius – 10
= 9m
Circumference of the inner circle = 2∏r
= 2 x 3.14 x 9
= 56.52 m
Circumference of the outer circle = 2∏r
= 2 x 3.14 x 19
= 119.32 m
Q16. How many times a wheel of radius 28 cm must rotate to go 352 cm?
Solution:-
Circumference of the wheel = 2∏r
= 2 x 22/7 x 28
= 176 cm
Number of rotation of the wheel = Total distance to be covered/Circumference of wheel
= 352 cm / 176 cm
= 200
Q17. The minute hand of a circular clock is 15 cm long How far does the tip of the minute hand move in 1 hour .
Solution:-
Circumference of the clock = 2∏r
= 2 x 3.14 x 15
= 94.2 cm.