Circumference of a Circle

Q.

The wheels of a car are of diameter $80$ cm each. How many complete revolutions does each wheel make in $10$ minutes when the car is travelling at a speed of $66$ km per hour?

Q.

If the perimeter of a circle is equal to that of square, then the ratio of their areas is:
(A) $22:7$
(B) $14:11$
(C) $7:22$
(D) $11:14$

Q.

In making 1000 revolutions, a wheel covers 88 km. The diameter of the wheel is

(a) 14 m (b) 24 m (c) 28 m (d) 40 m

Q. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

1. 2 units
2. 4 units
3. 6 units
4. π units

Q.

The difference between the circumference and radius of a circle is 37 cm. The area of the circle is

(a) 111${cm}^2\left(b\right)184{cm}^2\left(c\right)154{cm}^2\left(d\right)259c{m}^2$

Q.

The area of a circular playground is $22176m^2$. Find the cost of fencing this ground at the rate of Rs. 50 per metre.

Q.

The area of a circle is the same as the area of a square. Their perimeters are in the ratio.

(a) 1 : 1 (b) $\frac{2}{\sqrt{\pi }}$ (c) $\pi$ : 2 (d) $\sqrt{\pi }$ : 2

Q.

The radius of a wheel is 0.25 m. How many revolutions will it make in covering 11 km ?

(a) 2800 (b) 4000 (c) 5500 (d) 7000

Q.

The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 2 days.

[ Take $\pi =3.14$]

Q.

The area of a circle is 38.5 $c{m}^2$. The circumference of the circle is

(a) 6.2 cm (b) 12.1 cm (c) 11 cm (d) 22 cm

Q. The area of a circle is $38.5{\text{cm}}^2$. Its circumference is

1. $62\text{cm}$
2. $12.1\text{cm}$
3. $11\text{cm}$
4. $22\text{cm}$

Q.

A racetrack is in the form of a ring whose inner circumference is $352m$ and outer circumference is $396m.$ Find the width and the area of the track.

Q.

Give the relation between circumference and diameter of a circle.

Q.

A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase if he makes 2 rounds of the fence. Also, find the cost of the rope, if it costs Rs. 4 per meter. $(Take\pi =\frac{22}{7})$

Q.

The area of a circle is 49 $\pi$ $c{m}^2$. Its circumference is

(a) 7 $\pi$cm (b) 14 $\pi$cm (c) 21 $\pi$cm (d) 28 $\pi$cm

Q.

The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is

(a) 3 : 2 (b) 4 : 9 (c) 2 : 3 (d) 81 : 16

Q.

The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of the circle.

Q. The wheel of a motor cycle is of radius 35 cm. How many revolution per minute must the wheel make, so as to keep a speed of 66 km/h?

1. 400
2. 500
3. 600
4. 650

Q.

The wheels of a car make 2500 revolutions in covering a distance of 4.95 km. Find the diameter of a wheel.

Q.

A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.

Q. The circumference of a circle with radius $r$, is

1. $2\pi r$
2. 2$\pi r^2$
3. $\pi r$
4. $\pi r^2$

Q.

A path of 4 m width runs round a semi-circular grassy plot whose circumference is $163\frac{3}{7}m$. Find:

(i) The area of the path
(ii) The cost of gravelling the path at the rate of Rs. 1.50 per square metre
(iii) The cost of turfing the plot at the rate of 45 paise per $m^2$.

Q.

The wheels of the locomotive of a train are 2.1 m in radius. They make 75 reveloutions in one minute. Find the speed of the train in km per hour.

Q. If the circumference of a circle is $100\text{cm}$, then the side of a square inscribed in the circle is

1. $5\sqrt{2}\text{cm}$
2. $\frac{100}{\pi }\text{cm}$
3. $\frac{50\sqrt{2}}{\pi }\text{cm}$
4. $\frac{100\sqrt{2}}{\pi }\text{cm}$

Q.

The areas of two circles are in the ratio 4 : 9. What is the ratio between their circumferences ?

Q.

The diameters of the front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that a rear wheel makes to cover the distance which the front wheel covers in 800 revolutions.

Q.

A rectangular sheet of paper $40cm\times 22cm,$ is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is

(a) 3.5 (b) 7 (c) $\frac{80}{7}$ (d) 5

Q. Circular footpath of width 2 metres is constructed at the rate of Rs 20 per square metre, around a circular park of radius 1500m. Find the total cost of construction of the footpath.

Q.

A wheel has diameter 84 cm. Find how many complete revolutions must it make to cover 792 m.

1. 300

2. 250

3. 320

4. 400

Q.

The circumference of a circle is $88\text{cm}$. Its diameter is:

1. $28\text{cm}$

2. $42\text{cm}$

3. $56\text{cm}$

4. none of these