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)

class 7th math Perimeter and area solution of ncert exercise 11.3(5)

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.

class 7th math Perimeter and area solution of ncert exercise 11.3(7)

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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