11. Areas Related to Circles – SEBA Class 10 Mathematics Important Questions and Answers | HSLC Assam Board
Class 10 Mathematics Chapter 11. Areas Related to Circles – SEBA/HSLC Assam Board Important Questions & Answers
Chapter 11. Areas Related to Circles
SECTION = A
Question: Area of a sector of angle P (in degree) of a circle with radius R is : [SEBA 2015]
(a) 
(b) 
(c) 
(d) 
Solution: (d)
Question: If the sum of the areas of two circles with radii 
and 
is equal to the area of a circle of radius,then
(a) 
(b) 
(c) 
(d) 
Solution: (b)
Question: If the perimeter of a circle is equal to that of a square , then the ratio of their areas is :
(a) 22 : 7 (b) 14 : 11 (c) 7 : 22 (d) 11 : 14
Solution: (b) 14 : 11 .
[ let 
be the radius of the circle and 
be side of the square .
A/Q , 
]
Question: If the circumference of a circle is 44 cm , then its area is : [SEBA 2016]
(a) 276 
(a) 44 (c) 176 (d) 154
Solution: (d) 154 .
[ A/Q, 
cm
The area of the circle 
]
Question: The area of the circle that can be inscribe in a square of side 6 cm is : [ SEBA 2017]
(a) 
(b) 
(c) 
(d) 
Solution: (d)
[ The square of the side 
cm and the radius 
The area of the circle 
]
Question: If the circumference of a circle is 22 cm , then the area of a quadrant of the circle is : [SEBA 2018]
(a) 
(b) 77 (c) 
(d) 
Solution: (a)
[ A/Q , 
The area of a quadrant of the circle 
]
Question: The degree measure of the angle at the centre of a circle is 1 . The area of the sector is : [SEBA 2019]
(a) 
(b) 
(c) 
(d) 
Solution: (d)
Question: The degree measure of the angle at the centre of a circle is θ . The length of a arc of the sector is : [ SEBA 2020]
(a) 
(b) 
(c) 
(d) 
Where is the radius of the circle .
Solution: (b)
Question: If the sum of the circumference of two circles with radii 
and 
is equal to the circumference of a circle of radius , then
(a) 
(b) 
(c) 
(d) 
Solution: (a)
[ A/Q, 
]
Question: If the radius of a circle is doubled , then the ratio of the areas of the new circle to the area of the given circle is :
(a) 2 : 1 (b) 1 : 2 (c) 1 : 4 (d) 4 :1
Solution: (d) 4 :
[ Here , 
and 
]
Question: In the given figure , if the angle 30° , then the area of the shaded region (in cm square) is : [2011]
(a) 3.36 (b) 2.26 (c) 1.36 (d) 2.36
Solution: (d) 2.36 [ Here , 
cm and 
cm
The area of shaded region 
]
Question: If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then diameter of the larger circle (in cm) is : [CBSE 2012]
(a) 34 (b) 26 (c) 17 (d) 14
Solution: (b) 26
[ Here, 
A/Q , 
cm
Therefore , the diameter 
cm 
cm ]
Question: If 
is taken as 
, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution is : [CBSE 2013]
(a) 2.2 (b) 1.54 (c) 9.625 (d) 96.25
Solution: (b) 1.54
[ Here , Diameter 
cm and Radius 
Therefore, the distance covered by a wheel in one revolution 
cm 
]
Question: The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is :
(a) 30 cm (b) 40 cm (c) 50 cm (d) 20 cm
Solution: (c) 50 cm .
[ Here , 
cm and 
cm
A/Q , 
cm
Therefore , the diameter 
cm 
cm ]
Question: Area of a sector to circle of radius 36 cm is 
, then the length arc of the corresponding arc of the circle is :
(a) 
(b) 
(c) 
(d) 
Solution: (a)
[ Here , 
cm
A/Q, 
Therefore, the length arc of the corresponding arc of the circle 
]
Question: If the diameter of a semi-circular protractor is 14 cm , then its perimeter is : [CBSE 2009]
(a) 11 cm (b) 21 cm (c) 22 cm (d) 44 cm
Solution: (c) 22 cm .
[ Here , 
cm and 
The perimeter of a semi-circular 
]
SECTION = B
Question: In given figure , find the area of the sector of a circle with radius 4 cm .
Solution: Here , cm and 
Therefore, the area of the sector of a circle 
Question: Find the length of the arc of a circle of diameter 42 cm which subtends angle of 60° at the circle ? [CBSE 2012]
Solution: Here, Radius 
and 
Therefore, the length of the arc of a circle 
Question: Find the area of a quadrant of a circle whose circumference is 
. [ CBSE 2014]
Solution: Let, r be the radius of a circle .
A/Q , 
Therefore , the area of quadrant of the circle 
Question: The difference between the circumference and radius of a circle is 37 cm . Find the area of the circle . [ CBSE 2013]
Solution: Let, r be the radius of a circle .
A/Q , 
Therefore, the area of circle 
.
Question: Find the area of a sector of a circle of radius 28 cm and central angle 45° .
Solution: Here , 
cm and 
Therefore, the area of a sector of a circle 
Question: The radii of radius circles are 19 cm and 9 cm respectively . Find the radius of the circle which has circumference equal to the sum of the circumference of the two circles.
Solution: let be the radius of the new circle .
Here , 
cm and 
cm
A/Q , 
cm
Question: The length of the minute hand of a clock is 14 cm . Find the area swept by the minute hand in 5 minutes .
Solution : Here, 
The angle of swept in 5 minutes 
Therefore, the area swept by the minute hand in 5 minutes 
Question: Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60° .
Solution: Here , 
cm and
Therefore, the area of a sector of a circle 
Question: The cost of fencing a circular field at the rate of Rs. 24 per metre is Rs. 5280 , then find the radius of field .
Solution: let be the radius of the circular field .
The length of the fence field 
A/Q , 
Question: An umbrella has 8 ribs which are equally spaced and the umbrella to be a flat circle of radius 45 cm , find the area between the two consecutive ribs of the umbrella .
Solution: Here , 
cm
The area between the two consecutive ribs of the umbrella 
Question: If the area of a sector of a circle of radius 14 cm is 
. Find the length of the corresponding arc of the sector . [CBSE 2011]
Solution: Here , 
cm
A/Q , 
Therefore, the length of the corresponding arc of the sector 
SECTION = C
Question: A chord of a circle of radius 10 cm subtends a right angle at the centre . Find the area of the corresponding : (i) minor segment (ii) major sector . ( Use 
)
Solution : Here, 
The area of the minor segment of a circle 
(ii) Here, 
, 
Area of major sector of a circle 
Question: In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre . Find :
(i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord .
Solution: Here, Radius 
cm and 
(i) the length of an arc of a sector of a circle
(ii) the area of the sector formed by the arc
(iii) Here, OA = OB = 21 cm and 
So, OAB be an equilateral triangle .
Area of triangle OAB 
The area of segment formed by chord 
Area of sector – Area of triangle
Question: A chord of a circle of radius 15 cm subtends an angle of 60° at the centre . Find the areas of the corresponding minor and major segments of the circle . (Use 
and 
) [SEBA 2017]
Solution: Here , Radius 
cm ,
Area of the minor segment = Area of the sector – Area of the triangle formed by radius and chord
Area of major segment = Area of the circle – Area of the minor segment 
Question: A chord of a circle of radius 12 cm subtends an angle of 120° at the centre . Find the area of the corresponding segment of the circle . (Use and )
Solution : Here, 
and 
The area of the corresponding segment of the circle
Question: 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. 12.12 . Find :
(i) the total length of the silver wire required . (ii) the area of each sector of the brooch .
Fig. 12.12
Solution: (i) Here, diameter 
and Radius 
The circumference 
The length of the wire required to make 5 diameters 
Therefore, the total length of the silver wire required 
(ii) The angle of each brooch 
So, the area of each sector of the brooch 
SECTION = D
Question: A round table cover has six equal designs as shown in Fig. 12.14 . If the radius of the cover is 28 cm , find the cost of making the designs at the rate of Rs 0.35 per 
. (Use )
Solution: Here, 
and 
Area of a design part of the round table cover
Area of six design part of the round table cover 
Therefore, the cost of making the designs
Question: A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11) . Find : (i) the area of that part of the field in which the horse can graze . (ii) the increase in the grazing area if the rope were 10 m long instead of 5 m . (Use 
)
Solution : Since , ABCD is a square .
So, AB = BC = CD = AD = 15 cm
(i) Here, 
, 
Therefore, the area of the field in which the horse can graze 
(ii) Here, 
, 
and 
The increasing area of the field 
Question: In figure, a square OPQR is inscribe in a quadrant OAQB of a circle. If the radius of the circle is 
cm , find the area of the shaded region . [Use π = 3.14] [CBSE 2020 standard]
Solution: Given,
be a square .
So , 
cm
Area of square 
In
, we have 
cm
Radius 
cm
Area of the quadrant 
Therefore, the area of shaded region 
Q4. Find the area of the shaded design in figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter . [ Use 
]
Solution: Here ,
cm , Radius
cm
Area of unshaded region 
part and 
part
Area of ABCD 
Area of two semicircle
Area of unshaded region 
part and 
part .
Therefore, the area of shaded design
Area of square ABCD 
Area of 
Question: Calculate the area of the designed region in figure , common between the two quadrants of circles of radius 8 cm each . [CBSE 2012]
Solution: The radius of the quadrant of a circle 
cm and the side of the square cm
Therefore, the area of the shaded region Area of two quadrant of the circle – Area of the square
SECTION = E
Question: In figure, AB and CD are two diameter of a circle (with centre) perpendicular to each other and OD is the diameter of the smallest circle . If 
, find the area of the shaded region . [CBSE 2013,2020 Basic]
Solution: For big circle : Radius 
cm ,
Diameter 
cm
So, 
cm
For small circle : Diameter 
cm
and Radius 
cm
Area of small circle
Area of 
Area of semicircle 
The area of the shaded region
Area of small circle 
Area of semicircle – 
Question: In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter . Find the area of the shaded region . [CBSE 2014]
Solution: For ABCD quadrant :
Here , Radius 
cm
In∆ABC
, we have
cm
area of 
and Area of quadrant ABCD 
For semi-circle BEC :
Diameter 
cm ; Radius 
cm
Area of semi-circle BEC 
Area of shaded region ar() ar(semicircle BEC) – ar(quadrant ABCD)
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