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Important Questions(MCQ) for Area Related to Circle|Class 10 Maths

Given below are the Class 10 Maths Important Questions for Area Related to Circle
(a) Concepts questions
(b) Calculation problems
(c) Multiple choice questions
(d) Long answer questions
(e) Fill in the blank's

Multiple Choice Questions

Question 1
A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.
(a) 15.8 km/hr
(b) 16.2 km/hr
(c) 11 km/hr
(d) 18 km/hr

Question 2
A car has wheels which are 80 cm in diameter. How many complete revolutions does each wheel make in 10 minute when the car is travelling at a speed of 66km per hour?
(a) 5000
(b) 4375
(c) 5400
(d) 4400

Question 3
If the circumference of a circle and the perimeter of a square are equal, then
(A) Area of the circle = Area of the square
(B) Area of the circle > Area of the square
(C) Area of the circle < Area of the square
(D) Nothing definite can be said about the relation between the areas of the circle and square

Question 4The cost of fencing a circular field at the rate Rs24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m². Find the cost of ploughing the field.(Take Π=22/7)
a. Rs 2000
b. Rs 1900
c. Rs 1925
d. Rs 1800

Question 5
The side of a square is 10cm. The area of circumscribed and inscribed circles.?
(A) 157 cm², 78.5cm²
(B) 150 cm², 75cm²
(C) 147 cm², 78.5cm²
(D) 157 cm², 79.5cm²

Question 6
The sum of the radii of two circles is 140cm and the difference of their circumference is 88cm.Find the diameters of the circles.
(a) 150 cm, 88 cm
(b) 158 cm,122 cm
(c) 160 cm,120 cm
(d) 154cm, 126 cm

Question 7
If $\theta $ is the angle (in degrees) of a sector of a circle of radius r, then area of the sector is
(a) $ \frac {\pi r^2 \theta}{360}$
(b) $ \frac {\pi r^2 \theta}{180}$
(c) $ \frac {\pi r \theta}{180}$
(d) $ \frac {\pi r \theta}{90}$

Question 8
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles?
(a) 9 cm
(b) 10 cm
(c) 15 cm
(d) 11 cm
Question 9
Find the circumference of a circle whose area is 16 times the area of the circle with diameter 7cm
(a) 44 cm
(b) 88 cm
(c) 22 cm
(d) 66 cm
Question 10
If a square is inscribed in a circle, find the ratio of the areas of the circle and the square?
a. $ \pi : 2$
b. $ 2 : \pi$
c. $ \pi : 4$
d. $ 4 : \pi$

Question 11
If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius R, then
(A) $R_1 + R_2= R$
(B) $R_1^2 + R_2^2 = R^2$
(C) $R_1+ R_2 < R$
(D) $R_1^2 + R_2^2 < R^2$

Question 12
The area of a circle inscribed in an equilateral triangle is 154 cm². Find the perimeter of the triangle. [ Use Π=22/7]
(A) 72.7 cm
(B) 88 cm
(C) 75 cm
(D) 74.5 cm

Question 13
Which one of these is True
(A) Distance travelled by a circular wheel of diameter z cm in one revolution is $2 \pi z$ cm
(B) The area of the circle inscribed in a square of side x cm, $\pi x^2 \; cm^2$
(C) If the area of a circle is 154 cm² , then its perimeter is 55 cm
(D) The perimeter of a square circumscribing a circle of radius y cm is 8y cm

Question 14
A car travels 1km distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.
(A) 35.35 cm
(B) 34.35 cm
(C) 35.50 cm
(D) None of these

Question 15
Two circles touch externally. The sum of their areas is 58 cm² and the distance between their centres is 10 cm. Find the radii of the two circles
(A) 6 cm, 4 cm
(B) 7cm, 3cm
(C) 9 cm , 1 cm
(D) 8 cm ,2 cm

Calculation Problems

Question 16
A park is in the form of rectangle 120 m X100m. At the centre of the park there is a circular lawn. The area of park excluding lawn is 8700m². Find the radius of the circular lawn. [Use Π=22/7]
Question 17
The minute hand of a clock is 10cm long. Find out the area of the face of the clock described by the minute hand between 9 A.M. and 9.35A.M.
Question 18
Find the area of the sector of a circle with radius 4cm and of angle 30°. Also, find the area of the corresponding major sector. (Use Π=3.14)
Question 19
An elastic belt is placed round the rim of a pulley of radius 5cm. One point on the belt is pulled directly away from the centre O of the pulley until it is at P, 10cm from O. Find the length of the belt that is in contact with the rim of the pulley. Also, find the shaded area.
Question 20
In a circle with centre O and radius 5cm, AB is a chord of length 5√3cm the area of sector AOB.
Question 21
The perimeter of a certain sector of a circle of radius 5.6m is 27.2m. Find the area of the sector.
Question 22
A sector is cut off from a circle of radius 21cm. The angle of the sector is 120°. Find the length of its arc and the area.
Question 23
A sector of 56° cut out from a circle contains area 4.4cm². Find the radius of the circle

Answer
1. (a)
2. (b)
4. (b)
4. (c)
5. (a)
6. (d)
7. (a)
8. (b)
9. (b)
10. (a)
11. (b)
12. (a)
13. (d)
14. (a)
15. (b)
16.32.40
17. 183.3 cm²
18. 46.05 cm²
19. 25/3, 3√3 Π
20. 25Π/3
21. 44.8
22. 44 cm, 462 cm²
23. 3 cm

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