### NCERT Solutions for class 7 maths Exercise-11.3

# 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 =∏r^{2}

= 22/7 x 14 ^{2 }

= 22/ 7 x 196

= 22 x 28

= 616 mm^{2 }

*Diameter =49m*

= 49/2

= 24.5m

Area

^{2}

= 22/7 x ( 24.5 )^{2}

= 22/7 x 600.25

= 22 x 85.75

= 1886.5 m^{2}

*Radius =5 cm*

Area of the circle =∏r^{2}

=22/7 x 5^{2}

=22/7 x 25

=550/7

=78.57 cm^{2}

^{ }

*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 =∏r^{2}

=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.*

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*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

=∏(R^{2}-r^{2})

=3.14( 4^{2}-3^{2})

=3.14 (16 – 9 )

=3.14 x 7

=21.98 cm^{2}

*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:-*

* *

* *

* *

* *

* *

* *

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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/m ^{2}.*

*Solution:-*

Radius =1.6 m

= 1.6/2

=0.8 m

Area of the circular table – top = ∏r^{2}

=3.14 x 0.8 ^{2 }

=3.14 x 0.8 x 0.8

= 2.0096 m^{2}

Cost for polishing 1m^{2 } area= Rs.15

Cost for polishing 2.0096m^{2} 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 = ∏r^{2 }

=22/7 x 7^{2}

= 22/7 x 7 x 7

= 22 x 7

= 154 cm^{2}

The length of the each side of square = 44/4

= 11cm

= 11^{2}

=121cm^{2}

*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-*

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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 =∏r^{2}

=22/7 x 14 ^{2}

= 22/7 x 14 x 14

=22 x 2 x 14

=616 cm^{2}

Area of the 2 small circles = 2 x ∏r

=2 x (22/7 x 3.5^{2})

=2 x (22/7 x 12.25)

=2 x 38.5

=77cm^{2}

=3 x 1

=3cm^{2}

=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= side^{2 }

=6^{2}

=36cm^{2}

= 3.14 x 2^{2 }

= 3.14 x 4

= 12.56 cm^{2}

= 36 – 12.56

= 23.44 cm^{2}

^{ }

*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 = ∏r^{2}

= 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:-*

* *

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Radius of the flower bed = d/2

=66/2

=33m

Area of flower bed =∏r^{2}

=3.14 x 33 ^{2}

=3.14 x 1089

=3419.46 m

Area of the flower bed and path together= ∏r^{2}

=3.14 x 37^{2}

=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 m^{2}

*Q-14 A circular flower garden has an area of 314 m ^{2}.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:-*

* *

* *

* *

* *

* *

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Area of the circular flower garden = ∏r^{2}

314 = 3.14 x r^{2}

314/3.14 = r^{2}

R^{2 }= 100

R = √100

R = 10m

* *

*Q15. Find the circumference of the inner and the outer circles shown in the adjoining figure ? *

*Solution:-*

* *

* *

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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:-*

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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:-*

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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…

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