Chapter 9: Perimeter and Area

Solution:-

Given, the radius of the circle = 14 cm

Circumference of the circle = 2πr

= 2 × (22/7) × 14

= 2 × 22 × 2

= 88 cm

(b) 28 mm

Solution:-

Given, the radius of the circle = 28 mm

Circumference of the circle = 2πr

= 2 × (22/7) × 28

= 2 × 22 × 4

= 176 mm

(c) 21 cm

Solution:-

Given, the radius of the circle = 21 cm

Circumference of the circle = 2πr

= 2 × (22/7) × 21

= 2 × 22 × 3

= 132 cm

Given, the radius of the circle = 14 mm

Then,

Area of the circle = πr²

= 22/7 × 14²

= 22/7 × 196

= 22 × 28

= 616 mm²

(b) Diameter = 49 m

Given, the diameter of the circle (d) = 49 m

We know that radius (r) = d/2

= 49/2

= 24.5 m

Then,

Area of the circle = πr²

= 22/7 × (24.5)²

= 22/7 × 600.25

= 22 × 85.75

= 1886.5 m²

(c) Radius = 5 cm

Given, the radius of the circle = 5 cm

Then,

Area of the circle = πr²

= 22/7 × 5²

= 22/7 × 25

= 550/7

= 78.57 cm²

Solution:-

From the question, it is given that

Circumference of the circle = 154 m

Then,

We know that the circumference of the circle = 2πr

154 = 2 × (22/7) × r

154 = 44/7 × r

r = (154 × 7)/44

r = (14 × 7)/4

r = (7 × 7)/2

r = 49/2

r = 24.5 m

Now,

Area of the circle = πr²

= 22/7 × (24.5)²

= 22/7 × 600.25

= 22 × 85.75

= 1886.5 m²

So, the radius of the circle is 24.5, and the area of the circle is 1886.5.

Solution:-

From the question, it is given that

Diameter of the circular garden = 21 m

We know that radius (r) = d/2

= 21/2

= 10.5 m

Then,

Circumference of the circle = 2πr

= 2 × (22/7) × 10.5

= 462/7

= 66 m

So, the length of rope required = 2 × 66 = 132 m

Cost of 1 m rope = ₹ 4 [given]

Cost of 132 m rope = ₹ 4 × 132

= ₹ 528

Solution:-

From the question, it is given that

Radius of circular sheet R = 4 cm

A circle of radius to be removed r = 3 cm

Then,

The area of the remaining sheet = πR² – πr²

= π (R² – r²)

= 3.14 (4² – 3²)

= 3.14 (16 – 9)

= 3.14 × 7

= 21.98 cm²

So, the area of the remaining sheet is 21.98 cm².

Solution:-

From the question, it is given that

Diameter of the circular table = 1.5 m

We know that radius (r) = d/2

= 1.5/2

= 0.75 m

Then,

Circumference of the circle = 2πr

= 2 × 3.14 × 0.75

= 4.71 m

So, the length of the lace = 4.71 m

Cost of 1 m lace = ₹ 15 [given]

Cost of 4.71 m lace = ₹ 15 × 4.71

= ₹ 70.65

Solution:-

From the question, it is given that

Diameter of semi-circle = 10 cm

We know that radius (r) = d/2

= 10/2

= 5 cm

Then,

Circumference of the semi-circle = πr + 2r

= 3.14(5) + 2(5)

= 5 [3.14+ 2]

= 5 [5.14]

Therefore, the perimeter of the semicircle = 25.7 cm

Solution:-

From the question, it is given that

Diameter of the circular table-top = 1.6 m

We know that radius (r) = d/2

= 1.6/2

= 0.8 m

Then,

Area of the circular table-top = πr²

= 3.14 × 0.8²

= 3.14 × 0.8 ×0.8

= 2.0096 m²

Cost for polishing 1 m² area = ₹ 15 [given]

Cost for polishing 2.0096 m² area = ₹ 15 × 2.0096

= ₹ 30.144

Hence, the cost of polishing 2.0096 m² area is ₹ 30.144.

Solution:-

From the question, it is given that

Length of wire that Shazli took =44 cm

Then,

If the wire is bent into a circle,

We know that the circumference of the circle = 2πr

44 = 2 × (22/7) × r

44 = 44/7 × r

(44 × 7)/44 = r

r = 7 cm

Area of the circle = πr²

= 22/7 × 7²

= 22/7 × 7 ×7

= 22 × 7

= 154 cm²

Now,

If the wire is bent into a square,

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

= 11 cm

Area of the square = Length of the side of square²

= 11²

= 121 cm²

By comparing the two areas of the square and circle,

Clearly, the circle encloses more area.

Solution:-

From the question, it is given that

Radius of the circular card sheet = 14 cm

Radius of the two small circles = 3.5 cm

Length of the rectangle = 3 cm

Breadth of the rectangle = 1 cm

First, we have to find out the area of the circular card sheet, two circles and the rectangle to find out the remaining area.

Now,

Area of the circular card sheet = πr²

= 22/7 × 14²

= 22/7 × 14 × 14

= 22 × 2 × 14

= 616 cm²

Area of the 2 small circles = 2 × πr²

= 2 × (22/7 × 3.5²)

= 2 × (22/7 × 3.5 × 3.5)

= 2 × ((22/7) × 12.25)

= 2 × 38.5

= 77 cm²

Area of the rectangle = Length × Breadth

= 3 × 1

= 3 cm²

Now,

The area of the remaining part = Card sheet area – (Area of two small circles + Rectangle area)

= 616 – (77 + 3)

= 616 – 80

= 536 cm²