### Solved Examples

**Question 1: **Calculate the circumference of a circle of diameter 10 cm.

** Solution: **

We have, the radius of the circle = 10 cm

Circumference of a circle for the given diameter = $\pi$ d

= $\pi$ (10)

= 10 $\pi$

Substituting $\pi$ = 3.1415,

we get, circumference = 10 (3. 1415)

= 31.415

= **31.42 cm [ correct to two decimal places ]**

**Question 2: **Calculate the circumference of a circle of radius 8 cm

** Solution: **

**Method 1 :** We have the radius = 8 cm

Using the above formula, Circumference = 2 $\pi$ r

= 2 $\pi$ (8)

= 16 $\pi$

= 16 x 3.1415

= 50.254

**Circumference ** = **50.26 cm [ correct to 2 decimal places ]**

**Method 2 :** We have the radius = 8 cm

Therefore, diameter d = 2 r

= 2 (8)

= 16 cm

Using the above formula, Circumference = $\pi$ d

= $\pi$ (16)

= 16 $\pi$

= 16 x 3.1415

= 50.254

= 50.26 cm [ correct to 2 decimal places ]

**Question 3: **The circumference of a circle is 123.2 cm. Calculate the radius of the circle.

** Solution: **

Circumference = 123. 2 cm

We have the formula, Circumference C = 2 $\pi$ r

= 123.2 cm

**Method 1: **

2 $\pi$ r = 123.2 cm

=> r = $\frac{123.2}{2\pi}$

= 19.617

**radius = 19.62 cm [ correct to 2 decimal places ]**

**Method 2:** We have

the circumference, 2 $\pi$ r = 123.2

substituting $\pi$ = $\frac{22}{7}$, we get,

2 x $\frac{22}{7}$ r = 123.2

=> $\frac{44}{7}$ r = 123.2

=> r = 123.2 x $\frac{7}{44}$

**radius = 19.6 cm**

**Question 4: **The diameter of a bicycle wheel is 28 cm. How many revolutions will it make in moving 13.2 km.?

** Solution: **

Distance traveled by the wheel in one revolution = circumference of the wheel

= $\pi$ d

= $\frac{22}{7}$ (28)

= 88 cm

Total distance traveled by the wheel = 13.2 km

= 13.2 x 1000 m

= 13200 m

= 13200 x 100 cm

= 1320000 cm

Number of revolution made to travel 88 cm = 1

number of revolutions made to travel 1320000 cm = $\frac{1320000}{88}$

= 15,000

** Number of revolutions made = 15,000**

**Question 5: **The radius of a wheel is 35 cm and it takes 5 minutes to make 250
rotations. Find the speed of the wheel in km per hour. [ take $\pi$ =

$\frac{22}{7}$ ]

** Solution: **

Radius of the wheel = 35 cm

Circumference of the wheel = 2 $\pi$ r

= 2 x $\frac{22}{7}$ x 35

= 220 cm

= 2.2 m

Therefore, the distance covered in one rotation = 2.2 m

Distance covered in 250 rotations = 250 x 2.2

= 550 m

Therefore, the distance covered in 5 minutes = 550 m

=> distance covered in 1 min = $\frac{550}{5}$

= 110 m

Therefore, distance covered in 60 min = 110 x 60

= 6,600 m

= 6.6 km

( i. e ) distance covered in 1 hr = 6.6 km

=> ** speed of the wheel = 6.6 km / hr**

**Question 6: **The shape of a park is a rectangle bounded by semi circles at the ends, each of diameter 35 m, as shown in the figure. Find

a. the perimeter of the park.

b. Cost of fencing it at the rate of $\$$ 3 per m.

** Solution: **

Diameter of the park = 35 m

Length of the rectangular portion = 50 m

The above park consists of the rectangle and the two semi circles.

Therefore, **the boundary of the park = circumference of the two semi circles + 2 (length of the rectangle)**

Since the circumference of two semi circles = circumference of one full circle, we get

the **boundary of the park = circumference one circle + 2 (length of the rectangle)**

= $\pi$ d + 2 (50)

= $\frac{22}{7}$ (35) + 100

= 110 + 100 = 210 m

( i. e ) **the perimeter of the park = 210 m ------------------------------- ( a )**

Cost of fencing @ $\$$ 3 per m = 210 x 3

= $\$$ 610

** The cost of fencing = $\$$ 610 ----------------------------- ( b )**