Exercise 13.5

1. Find the circumference of a circle whose radius is-

2. Find the circumference of circle whose diameter is-

3. (i) Taking π = 3.14, find the circumference of a circle whose radius is

(ii) Calculate the radius of a circle whose circumference is 44cm?

Answer:

Circumference (C) = cm

C = 2πr

= 2 × 227 ×

44 = /7 × r

r = 44 × 744

r = cm

4. If the circumference of a circle is 264 cm, find its radius. Take π = 227.

Answer:

Circumference (C) = cm

C = 2πr

264 = 2 × 227 × r

264 = /7 × r

r = 264 × /44

r = × 7

r = cm

5. If the circumference of a circle is 33 cm, find its diameter.

Answer:

Circumference (C) = cm

C = πd

= 227 × d

d = 33 × 722

d = × 7/

d = cm

6. How many times will a wheel of radius 35cm be rotated to travel 660 cm? (Take π = 227).

Answer:

Radius (r) = cm

Circumference of wheel (C) = 2πr

C = 2 × 227 ×

C = 2 × 22 ×

C = cm

Total distance to travel = cm

Number of rotations = Total distance ÷ Circumference

Number of rotations = 660 ÷

Number of rotations = times

7. The ratio of the diameters of two circles is 3 : 4. Find the ratio of their circumferences.

Answer:

Let the diameters be d₁ and d₂.

Given, d₁ : d₂ = :

Let d₁ = and d₂ =

Circumference of first circle (C₁) = πd₁ = π ×

Circumference of second circle (C₂) = πd₂ = π ×

Ratio of circumferences = C₁ : C₂ = (π × ) : (π × )

Ratio = 3x :

Ratio = 3 :

8. A road roller makes 200 rotations in covering 2200 m. Find the radius of the roller.

Answer:

Number of rotations =

Total distance covered = m = cm

Distance covered in one rotation = Total distance ÷ Number of rotations

Distance covered in one rotation = 220000 ÷

Distance covered in one rotation = cm

This distance is the circumference of the roller.

Circumference (C) = 2πr

= 2 × 227 × r

1100 = / × r

r = 1100 × 744

r = × 7

r = cm

9. The minute hand of a circular clock is 15 cm. How far does the tip of the minute hand move in 1 hour? (Take π = 3.14)

Answer:

Radius of the circular path (r) = Length of minute hand = cm

In 1 hour, the minute hand completes one full rotation.

Distance moved by the tip = Circumference of the circle

C = 2πr

C = 2 × ×

C = cm

The tip of the minute hand moves cm in 1 hour.

10. A wire is bent in the form of a circle with radius 25 cm. It is straightened and made into a square. What is the length of the side of the square?

Answer:

Radius of the circle (r) = cm

Length of the wire = Circumference of the circle

C = 2πr

C = 2 × 227 ×

C = / cm

Perimeter of square = × side

1100/7 = 4 × side

side = 1100/7 ÷

side = /7

side ≈ cm (rounded to two decimal places)