# 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:

1. 14 cm

Circumference of the circle =2∏r

=2 x (22 /7 ) x 14

= 2 x 22 x 2

= 88 cm

1. 28 cm

Circumference of the circle= 2∏r

=2 x (22/7) x 28

=176 cm

1. 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 :

Area of the circle =∏r2

= 22/7 x 14 2

= 22/ 7 x 196

= 22 x 28

= 616 mm2

1. 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

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:-

=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:-

= 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

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:-

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:-

= 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.

NCERT Solutions for class 7 Science Chapter-14

NCERT Solutions for class 7 maths Chapetr- 11 Perimeter and area     Exercise-11.3 Q-1 Find the circumference of the circle with…