Solution of NCERT Exercise 11.3
Perimeter and Area 7th Math
Solution of NCERT Exercise 11.3
Question (1) Find the circumference of the circles with the following radius (take `pi = 22/7`).
(a) 14 cm
(b) 28 mm
(c) 21 cm
Solution:
(a) Given, Radius of the circle = 14 cm
Therefore, Area of circle =?
We know that,
Area of a circle = `pi r^2`
=` 22/7` × (14 cm)2
=`22/7` × 14 cm × 14 cm
=22 × 2 × 14 cm2
= 616 cm2
Thus, Area of the given circle = 616 cm2Answer
(b)Given, Radius of circle = 28 mm
Thus, Area of the circle = ?
We know that,
Area of a circle = `pi r^2`
= `22/7` × (28 mm)2
= `22/7` × 28 mm × 28 mm
= 22 × 4 × 28 mm2
= 2464 mm2
Thus, Area of given circle
=2464 mm2 Answer.
(c) Given, Radius of the circle = 21 cm
Thus, Area of the circle =?
We know that,
Area of a circle = `pi r^2`
= `22/7` × (21 cm)2
=` 22/7` × 21 cm × 21 cm
= 22 × 63 cm2
= 1386 cm2
Thus, Area of the circle = 1386 cm2 Answer.
Question (2) Find the area of the following circles given that
(a) Radius = 14 mm (Take 𝜋 = `22/7`)
Solution :
Given,
Radius of the circle = 14 mm
Therefore,
Area of circle = ?
We know that;
Area of a circle = 𝞹 r2
=`22/7` × (14 mm)2
=`22/7` ×14 mm × 14 mm
= 22 ×28 mm2
=616 mm2
Thus, Area of the circle = 616 mm2Answer.
(b) Diameter = 49 m
Solution:
Given,
Diameter of the circle = 49 m.
∵ Radius of the circle = Diameter/2
= `49/2` m
⇒ Radius of the circle =24.5 m
Thus, area of circle = ?
We know that,
Area of a circle = 𝞹 r2
=`22/7` × (24.5 m)2
= `22/7` × 24.5 m × 24.5 m
= 22 × 3.5 m × 24.5 m
= 1886.5 m2
Thus,
Area of the given circle = 1886.5 m2 Answer
(c) Radius = 5 cm
Solution:
Given,
Radius of the circle = 5 cm.
∵ Area of the circle = ?
We know that,
Area of a circle = π r2
=`22/7` × (5cm)2
= `22/7` × 25 cm2
= `550/7` cm2
= 78.57 cm2
Thus,
Area of the given circle = 78.57 cm2 Answer
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`)
Solution:
Given,
Circumference of the circle = 154 m.
∵ Radius of the circle = ?
And Area of circle =?
We know that,
Circumference of a circle = 2π r
⇒ 154m = `2 xx 22/7 xx r`
⇒ `2xx22/7 xx r` = 154 m
⇒ 2 × 22 × r = 154 m × 7
⇒ r = `(154 m xx 7)/(2 xx 22)` m
= `(77 xx 7)/22 ` m
= `49/2` m
⇒ r = 24.5 m
Now, we Know that,
Area of a circle = π r2
∴ Area of the given circle = `22/7` × (24.5 m)2
= `22/7` × 24.5 m × 24.5 m
= 1886.5 m2
Thus, Radius of the circle = 24.5 m and area of the circle = 1886.5 m2Answer.
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 cost Rs. 4 per metre. ( take π = `22/7`)
Solution:
Given,
Diameter of the circular garden = 21 m
Length of rope to two round of fencing the garden = ?
And, Rate of rope = ₹ 4 per metre
∴ Cost of rope for fencing =?
We know that,
Circumference of a circle = 2 π r = π d
=`22/7` × 21 m = 66 m
Thus circumference of garden = 66m
Since, two rounds of fencing is to be done
Therefore,
Length of rope = Circumference × 2
= 66 m × 2
= 132 m
Therefore, length of rope required for 2 round of fencing = 132 m.
Now,
∵ Cost of 1 metre of rope = ₹ 4.00
∴ Cost of 132 m of rope = ₹ 4.00 × 132
= ₹ 528.00
Thus, Length of the rope required for fencing = 132 m; and cost of rope = ₹ 528.00 Answer
Question (5) From a circular sheet of radius 4cm, a circle of radium 3 cm is removed. Find the area of the remaining sheet.(Take π = 3.14)
Solution:
Given,
Radius of a circular sheet = 4 cm
Radium of circle removed = 3 cm
Therefore, Area of remaining circular sheet = ?
We know that,
Area of a circle = π r 2
Thus,
Area of a circular sheet = 3.14 × (4 cm) 2
= 3.14 × 16 cm 2
= 50.24 cm 2
Thus,
Area of circular sheet = 50.24 cm2
Now,
Area of circle removed = π r2
= 3.14 × (3 cm)2
= 3.14 × 9 cm2
= 28.26 cm2
Thus Area of circle removed = 28.26 cm2
Now,
Area of circular sheet after removing circle
= Area of whole circular – Area of circle removed
= 50.24 cm2 – 28.26 cm2
= 21.98 cm2
Thus,
Area of remaining circular sheet = 21.98 cm2 Answer
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 metre of the lace cost Rs. 15. (Take π = 3.14)
Solution:
Given, Diameter of circular table cover = 1.5 m
Rate of lace = ₹ 15 / metre
Therefore, Length of lace to put on the edge of circular table and Cost of lace =?
[Strategy to solve this question: Since lace is to be put on circular table cloth. Thus circumference of table cloth will be equal to length of lace.]
Now,
We know that,
Circumference of circle = 2 π r = π d
Thus,
Circumference of circular table cloth = 3.14 × 1.5 m
= 4.71 m
Thus,
Circumference of circular table cloth = 4.71 m
Since, lace is to be put on the edge of table cloth.
Thus,
Length of the lace = circumference of table cover
= 4.71m
Now Since cost of 1 m of lace = ₹ 15
∴ Cost of 4.71 m of lace = ₹ 15 × 4.71
= ₹ 70.65
Thus,
Length of lace required = 4.71 metre and cost of lace = ₹ 70.65 Answer
Question (7) Find the perimeter of the adjoining figure which is a semicircle including its diameter.
Solution:
Given,
Diameter of semicircle = 10 cm
∴ Radius of semicircle = `10/2`= 5 cm.
Perimeter of semicircle =?
We know that,
Circumference of circle = 2 π r
Therefore, Circumference of semicircle =`1/2` × 2π r
= πr
= `22/7` × 5 cm
= `110/7` cm = 15.17 cm
Now, Perimeter of semicircle
= Circumference of semicircle + Diameter
= 15.71 cm + 10 cm
= 25.71 cm
Therefore, Perimeter of given semicircle = 25.71 cm Answer
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