CBSE Class 10 Maths HOTs Area related to Circle

Very Short Answer Type Questions

Question. 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?
Answer : 4375

Question. Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.
Answer : 33 cm

Question. A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of the its wheels.
Answer : 35.35

Question. A circular park is surrounded by a rod 21 m wide. If the radius of the park is 105 m, find the area of the road .
Answer : 15246 cm²

Question. Find the area of sector of a circle with radius 6 cm and sector angle is 60°.
Answer : 1327 cm2

Question. A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.
Answer : 2618 m²

Question. A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be ₹2640 at the rate of ₹12 per metre. Then, the field is to be thoroughly ploughed at the cost of ₹0.50 per m². What is the amount required to plough the field?
Answer : Rs. 1925

Question. A pendulum swings through an angle 60° and describes an arc 8.8 cm in length ,then find the legth of pendulum
Answer : 8.4 cm

Question. The area of enclosed between the concentric circles is 770 cm². If the radius of the outer circle is 21 cm, find the radius of the inner circle.
Answer : 14 cm

Question. The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of the circle
Answer : 24.64 cm

Question. Find circumference of a circle whose area is 314 cm2. (Given π = 3.14)
Answer : 62.8 cm

Question. Rear wheel of a motor cycle is of radius 35 cm. It is assumed that the speed of the motor cycle is fully depend on the rpm of the rear wheel and no loss of energy. How many revolutions per minute (rpm) must the wheel make so as to keep a constant speed of 66 km/hr. (Take π = 22/7 )
Answer : 500rpm

Question. Find the area of a sector of a circle of radius 28 cm and central angle 45˚. (Take π = 22/7 )
Answer : 308𝑐𝑚²

Question. A chord of a circle of radius 10 cm subtends right angle at the centre of the circle. What will be the area of the corresponding major sector. (Given π = 3.14)
Answer : 235.5𝑐𝑚²

Question. Area of a sector is one- twelfth that of the complete circle. Find the angle of the sector.
Answer : 30

Question. Find area of a sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.
Answer : 8.7𝑐𝑚²

Question. An arc of a circle of length 5π cm bounds a sector whose area is 20π cm². Find the radius of the circle.
Answer : 8cm

Question. State the following statement is “True” or “False”.
“If the perimeter and area of a circle are numerically equal, then the radius of the circle is 2 units”.
Answer : True

Question. Say the following statement is “True” or “False”. Write reason for your answer.
“Area of a segment of a circle is less than the area of its corresponding sector.”
Answer : false

Question. If the perimeter of a semi-circular protractor is 66 cm, find the length of the straight-line part of the protractor. (Take π = 22/7 )
Answer : 21cm

Question. A race track is in the form of a ring whose inner circumference is 352m and the outer circumference is 396m.Find the width of the track.
Answer : 7 m

Question. The chord of a circle of radius 10 cm subtends a right angle at its centre. Find the length of the chord. (Given π = 3.14)
Answer : 102 cm

Question. The difference between circumference and radius of a circular field is 37 m. Find the area of the field. (Hint: π = 22/7 )
Answer : 157 sq.cm

Question. Find the area of a sector whose perimeter is four times its radius r units.
Answer : 𝑟² sq.units

Question. If the area of a circle inscribed in an equilateral triangle is given as 48π square units, then what is the perimeter of the triangle?
Answer : 48√3 units

Question. It is given that area of a circle is equal to the sum of the areas of two circles of diameters 10cm and 24cm. then find the diameter of the larger circle.
Answer : 26cm.

Question. A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 600 at its centre. Find the radius of the circle.
Answer : 60/𝜋 cm

Question. A wheel has diameter 84cm.Find how many complete revolutions must it take to cover 792m.
Answer : 300

Question. A car travels 1 km distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.
Answer : 35.35 cm

Question. Find the area of the shaded region in the given figure, ¡f radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC = 40°.

Answer : (153/4) cm²

Question. An archery target has three regions formed by the concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions
Answer : 1:3:5

Question. The cost of fencing a circular field at the rate of Rs 36 per m is 11880.The field is to be ploughed at the rate of Rs. 0.60 per m2.Then find the cost of ploughing the field.
Answer : Rs. 5197.5

Question. Find the ratio of the areas of two sectors 𝑆₁ and 𝑆₂.

Answer : 4:5

Question. From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the figure. Find the area of the remaining portion of the square.

Answer : (68/7)cm²

Please refer to link below to download pdf file of CBSE Class 10 Area related to Circle HOTs

Hot questions for bright students
Area related to circles

2 marks Questions

Q.1. A race track is in the form of a ring whose circumference is 352m, and the outer circumference is 396m. Find the width of the track?

Q.2. A wheel has diameter 84cm. Find how many complete revolution must it take to cover 792 meters.
Sol. Let r be the radius of the wheel.
Then , Diameter = 84 cm
Þ 2r = 84
Þ r = 42cm
\ Circumference of the wheel = 2pr cm

= 2 x 22/7 x 42 cm
= 264 cm
= 2.64m
So, the wheel comes 2.64 metres in one complete revolutions.
\ Total number of revolutions in covering 792 metres = 792/2.64 = 300
Hence , the wheel takes 300 revolution in covering 792 metres.

Q.3. A chord AB of a circle of radius 15cm makes and angle of 600 at the center of the circle . Find the area of the minor segment. 

ADDITIONAL QUESTIONS

 Areas Related to Circles

1. A square circumscribes a circle of radius 5 cm. Find the length of the diagonal of the square.

2. The perimeter of a protractor is 36 cm. Find its diameter.

3. The length of a minute hand of a clock is 7cm. What is the area swept by it from7.00 am to 7.15 am?

4. If the perimeter and area of a circle are numerically equal then what is its radius?

5. In the given figure, ÐBAC = 90°, AB = 6cm, AC = 8 cm. Two semi circles with diameter AB and AC are drawn. Find the area of the shaded region.