WORD PROBLES ON CIRCUMFERENCE OF A CIRCLE

Problem 1 :

The circumference of circle whose diameter is 14 cm will be ________.

Solution :

Given, diameter = 14 cm

Radius r = 14/2 = 7 cm

Circumference = 2πr

= 2 × 22/7 × 7

= 44 cm

So, the circumference of circle whose diameter is 14 cm will be 44 cm.

Problem 2 :

What is the circumference of a circular disc of radius 14 cm?

Solution :

Given, Radius r = 14 cm

Circumference = 2πr

= 2 × 22/7 × 14

= 88 cm

So, the circumference of a circular disc is 88 cm.

Problem 3 :

The circumference of a circle is 31.4 cm. find the radius. (Take π = 3.14)

Solution :

Given, circumference of the circle = 31.4 cm

2πr = 31.4

2 × 3.14 × r = 31.4

6.28 × r = 31.4

r = 31.4/6.28

r = 5 cm

So, radius of the circle is 5 cm.

Problem 4 :

If the circumference of a circle with radius 3.5 cm is 22 cm. Find the perimeter of the semicircle. (Take π = 3.14)

Solution :

Circumference = 22 cm

Radius r = 3.5 cm

Perimeter of the semicircle = πr + 2r

= r (π + 2)

= 3.5 (3.14 + 2)

= 3.5 ×5.14

= 17.99 cm

So, perimeter of the semicircle is 17.99 cm.

Problem 5 :

If the circumference of a circle is 132 cm. Find the perimeter of the semicircle. (Take π = 3.14)

Solution :

Circumference of a circle = 132 cm

2πr = 132

r = 132/2π

r = 132/ (2 × 3.14)

r = 132/6.28

r = 21.01 cm

Perimeter of the semicircle = πr + 2r

= r (π + 2)

= 21.01 (3.14 + 2)

= 21.01 × 5.14

= 107.99 cm

= 108 cm

So, perimeter of the semicircle is 108 cm.

Problem 6 :

The radii of two circles are in the ratio 2: 3. What is the ratio of their circumference?

Solution :

Let the radius of two circle be 2x and 3x respectively.

Circumference of a circle = 2πr

Circumference of first circle = 2 × π × 2x

= 4πx

Circumference of second circle = 2 × π × 3x

= 6πx

Ratio of circumference of two circles = 4πx/6πx

= 4/6

= 2/3

Hence, ratio of their circumference is 2: 3.

Problem 7 :

A 44 m long wire is bent to form a circle. Find the diameter of the circle.

Solution :

Given, length of the wire = 44 cm

Circumference of the circle = length of the wire = 44 cm

2πr = 44

2 × 22/7 × r = 44

r = 44 × 7/44

r = 7 cm

Diameter = 2 × radius

= 2 × 7

Diameter = 14 cm

So, the diameter of the circle is 14 cm.

Problem 8 :

A wire is in the form of a circle of radius 35 m. It is now bent in the form of an equilateral triangle. Find the side of the triangle.

Solution : 

Given, the radius of the circle = 35 m

Circumference of circle = 2πr

= 2 × 22/7 × 35

= 220 m

The circumference of circle = perimeter of equilateral triangle

Let, one side of an equilateral triangle be x.

Perimeter of equilateral triangle = 3x

3x = 220

x = 220/3

x = 73.33 m

So, the each side of an equilateral triangle is 73.33 m.