CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set A

Question : The angle described by the minute hand between 4.00 pm and 4.25 pm is 
a. 90⁰
b. 150⁰
c. 125⁰
d. 100⁰

Answer : B
Explanation: Time duration between 4.00 pm and 4.25 pm = 25 minutes
Angle described by minute hand in 60 minutes =360 ⁰ 
Angle described by minute hand in 25 minutes =360 ⁰/60⁰×25=150⁰

CASE STUDY

In a Jewellery work shop, a brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig.

Question : What is the radius of the circle?
a) 35/2 mm
b) 5/2 Mm
c) 35mm
d) 10mm
Answer : A

Question : What is the circumference of the brooch?
a) 100mm
b) 110 mm
c) 50mm
d) 10mm
Answer : B

Question : What is the total length of silver wire required ?
a) 528 mm
b) 825mm
c) 285mm
d) 852mm
Answer : C

Question : What is the area of each sector of the brooch?
a) 385/2 mm²
b) 358/2 mm²
c) 585/2 mm²
d) 385/4 mm²
Answer : D

Very Short Answer type Questions

Question : Find the difference of the areas of two segments of a circle formed by a chord of length 5cm subtending an angle of 900 at the centre.
Answer : 25/4 (π + 2)

Question : A bicycle wheel makes 5000 revolutions in moving 11km.Find the diameter of the wheel.
Answer : 70 cm

Question : A ceiling fan has 3 wings. Find the length of the arc described between two consecutive wings, where length of each wing is 0.98 m.
Answer : 2.05 m

Question : A chord AB of a circle of radius 10 cm makes a right angle at the centre of the circle. Find the area of the minor and major segments.
Answer : 28.5cm², 285.5cm²

Question : Two circles touch internally. The sum of their areas is 116 π 𝑐𝑚² and the distance between their centres is 6cm. Find the radii of the circles.
Answer : 10 cm, 4cm

Question : Find the difference of the areas of a sector of angle 1200 and its corresponding major sector of a circle of radius 21 cm.
Answer : 462𝑐𝑚²

Question : If the difference between the circumference and area of a circle is 37 cm, find its area.
Answer : 154cm²

Question : 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.
Answer : 15.84 km/hr

Question : Four poles are erected at four corners of a rectangular field of dimensions 80 m by 50 m. Vasanthi tethered a cow at one corner of the field with a rope. After tying the length of rope from pole to cow is 7 m and Rajan tethered a buffalo at another pole of the same field and the length of rope from pole to animal is 6.3 m.
Answer the following questions.
i. How much area of the rectangular field did the cow graze?
ii. Find the ratio of grazing areas of the field by the cow and buffalo.
Answer : 38.5sq.cm, 100:81

Question : A square is inscribed in a circle. Calculate the ratio of area of circle to that of square.
Answer : Π :2

Question : A chord of a circle of radius 10cm subtends a right angle at the centre.find
(1) area of the minor sector (2) area of the minor segment
(2) area of the major sector (4) area of the major segment
Answer : 78.5, 28.5, 235.5, 285.5