• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

  • NCERT Solutions
    • NCERT Solutions for Class 12 English Flamingo and Vistas
    • NCERT Solutions for Class 11 English
    • NCERT Solutions for Class 11 Hindi
    • NCERT Solutions for Class 12 Hindi
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

GSEB Solutions for Class 10 mathematics – Areas Related to a Circle

Contents

GSEB Solutions for Class 10 mathematics – Areas Related to a Circle (English Medium)

GSEB SolutionsMathsScience

Exercise-13.1

Question 1:

Find the circumference and the area of the circle whose radius is 8.4 cm.

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.1)-1

Question 2:

Find the circumference of the circle whose area is 38.5 m2.

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.1)-2

Question 3:

The inner circumference of a circular race track is 44 m less than the outer circumference. If the outer circumference is 396 m, then find the width of the track.

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.1)-3

Question 4:

The radius of the wheel of a truck is 7 cm. It takes 250 revolution per minute. Find the speed of the truck in km/hr.

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.1)-4

Exercise-13.2

Question 1:

An arc of a circle whose radius is 21 cm subtends an angle of measure 120 at the centre. Find the length of the arc and area of the sector.

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.2)-1

Question 2:

The radius of a circular ground is 63 m. There is 7 m wide road inside the ground as shown in figure 13.10. The blue coloured portion of the road, shown in figure 13.10 is to be repaired. If the rate of repair work of the road costs ₹ 25 per m2, find the total cost of repair.
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle -1
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.2)-2

Question 3:

A regular hexagon of side 10 cm is cut from a plane circular sheet of radius 10 cm as shown in the figure 13.11. Find the area of the remaining part of the sheet. (\(\sqrt{3}\) = 1.73) (π = 3.14).
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle -2
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.2)-3

Question 4:

The length of a minute hand of a circular dial is 10 cm. Find the area of the sector formed by the present position and position five minute of the minute hand. (π = 3.14)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.2)-4

Question 5:

The radius of a field in the form of a sector is 21 m. The cost of constructing a wall around the field is ₹ 1875 at the rate of ₹ 25 per meter. If it costs  ₹ 10 per m2 to the field. what will be the cost of tilling the whole field ?

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.2)-5

Question 6:

The length of a side of a square field is 20 m. A cow is tied at the corner by means of a 6 m long rope. Find the area of the field which  the cow can graze. Also find the increase in grazing area, if the length of the rope is increased by 2 m.(π = 3.14)
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle -3
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.2)-6

Question 7:

A chord of a circle of radius 42 cm subtends an angle of measure 60 at the centre. Find the area of the minor segment of the circle. (\(\sqrt{3}\) = 1.73)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.2)-7

Question 8:

A chord of a circle, of length 10 cm, subtends a right angle at the centre. Find the areas of the minor segment and the major segment formed by the chord. (π = 3.14)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.2)-8

Exercise-13.3

Question 1:

A rectangle whose length and breadth are 12 cm and 5 cm respectively is inscribed in a circle. Find the area of the blue coloured region, as shown in the figure 13.19.
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 4

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.3)-1

Question 2:

ABCD, square park, has each side of length 80 m. There is a flower bed at each corner in the form of a sector of radius 7 m, as shown in figure 13.20. Find the area of the remaining part of the park.
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 5

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.3)-2

Question 3:

What will be the cost of covering the in figure 13.21 with a silver foil if the ₹ 100 per m2 ? (π = 3.14)
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 6
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.3)-3

Question 4:

ABCD is a square plate of 1 m length. As shown in figure circles are drawn with their center at A, B, C, D respectively, each with radius equal to 42 cm. The blue coloured part at each corner, as shown in the figure 13.22 is cut. What is the area of the remaining portion of the plate ?
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 7
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.3)-4

Question 5:

\(\overline{OA}\)  and \(\overline{OB}\)  are two mutually perpendicular radii of a circle of radius 10.5 cm. D ∈ \(\overline{OB}\)  and OD = 6 cm. Find the area of blue coloured region shown in figure 13.23.
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 8
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13.3)-5

Exercise-13

Question 1:

The area of a circular park is 616 m2. There is a 3.5 m wide track around the park running parallel to the boundary. Calculate the cost of fencing on the outer circle at the rate of ₹ 5 per meter.

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-1

Question 2:

A man is cycling in such a way that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, then how much distance will he cover in 2 hours ?

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-2

Question 3:

If a chord \(\overline{AB}\)  of ⨀(O, 20) subtends right angle at O, find the area of the minor segrnent.

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-3

Question 4:

There are two arcs \(\overset\frown{APB}\) of ⨀(O, OA) and \(\overset\frown{AQB}\)  of (M, MA) as shown in figure 13.24. Find the area enclosed by two arcs.
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 9
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-4

Question 5:

The length of a side of a square garden ABCD is 70 m. A minor segment of ⨀(O, OA) is drawn on each of two opposite sides for developing lawn, as shown in figure 13.24. Find the area of the lawn.
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 10
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-5

Question 6:

ABCD is a square of side 20 cm. Find the area of blue coloured region formed by the semi-circles drawn on each side as shown in figure 13.26. (π = 3.14)
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 11
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-6

Question 7:

On a circular table top of radius 30 cm a design is formed leaving an equilateral triangle inscribed in a circle. Find the area of the design. (π = 3.14)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-7.1
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-7.2

Question 8:

Figure 13.27 shows a kite formed by a square PQRS and an iscosceles right triangle ARB whose congruent sides are 5 cm long. \(\overset\frown{APB}\) is an arc of a ⨀ (R, 42). Find the area of the blue coloured region.
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 12
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-8

Question 9:

In figure 13.28, ABCD is a square with sides having length 8 cm. Find the area of the blue coloured region. (π = 3.14)
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 13
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-9

Question 10:

A circle is inscribed in ∆PQR where m∠Q = 90, PQ = 8 cm and QR = 6 cm. Find the area of the blue coloured region shown in figure 13.29. (π = 3.14)
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle - 14
Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-10

Question 11:

Select a proper option (a), (b), (c) or (d) from given options :

Question 11(1):

If an arc of a circle subtends an angle of measure θ at the centre, then the area of the minor sector is ……..

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.1

Question 11(2):

The area of a sector is given by the formula ……
(r is the radius and l is the length of an arc.)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.2

Question 11(3):

\(\overline{OA}\) and \(\overline{OB}\) are the two mutually perpendicular radii of a circle having radius 9 cm. The area of the minor sector corresponding to ∠AOB is ………. cm2. (π = 3.14)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.3

Question 11(4):

A sector subtends an angle of measure 120 at the centre of a circle having radius of 21 cm. The area of the sector is ……. cm2

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.4

Question 11(5):

If the area and the circumference of a circle are numerically equal, then r ………..

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.5

Question 11(6):

The length of an arc subtending an angle of measure 60 at the centre of a circle whose area is 616 is ………….

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.6

Question 11(7):

The area of a minor sector of ⨀(O, 15) is 150. The length of the corresponding arc is …… . (π = 3.14)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.7

Question 11(8):

If the radius of a circle is increased by 10 %, then corresponding increase in the area of the circle is ………. (π = 3.14)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.8

Question 11(9):

If the ratio of the area of two circles is 1 : 4, then the ratio of their circumference …………

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.9

Question 11(10):

The area of the largest triangle inscribed in a semi-circle of radius 8 is …………

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.10

Question 11(11):

If the circumference of a circle is 44 then the length of a side of a square inscribed in the circle is ……..

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.11

Question 11(12):

The length of minute hand of a clock is 14 cm. If the minute hand moves from 2 to 11 on the circular dial, then area covered by it is ……… cm2.

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.12

Question 11(13):

The length of minute hand of a clock is 15 cm. If the minute hand moves for 20 minutes on a circular dial of a clock, the area covered by it is …….. cm2. (π = 3.14)

Solution :
GSEB Solutions for Class 10 mathematics - Areas Related to a Circle-ex(13)-11.13

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers
  • The Summer Of The Beautiful White Horse Answers
  • Job Application Letter class 12 Samples
  • Science Lab Manual Class 9
  • Letter to The Editor Class 12 Samples
  • Unseen Passage For Class 6 Answers
  • NCERT Solutions for Class 12 Hindi Core
  • Invitation and Replies Class 12 Examples
  • Advertisement Writing Class 11 Examples
  • Lab Manual Class 10 Science

Recent Posts

  • Understanding Diversity Question Answer Class 6 Social Science Civics Chapter 1 NCERT Solutions
  • Our Changing Earth Question Answer Class 7 Social Science Geography Chapter 3 NCERT Solutions
  • Inside Our Earth Question Answer Class 7 Social Science Geography Chapter 2 NCERT Solutions
  • Rulers and Buildings Question Answer Class 7 Social Science History Chapter 5 NCERT Solutions
  • On Equality Question Answer Class 7 Social Science Civics Chapter 1 NCERT Solutions
  • Role of the Government in Health Question Answer Class 7 Social Science Civics Chapter 2 NCERT Solutions
  • Vital Villages, Thriving Towns Question Answer Class 6 Social Science History Chapter 9 NCERT Solutions
  • New Empires and Kingdoms Question Answer Class 6 Social Science History Chapter 11 NCERT Solutions
  • The Delhi Sultans Question Answer Class 7 Social Science History Chapter 3 NCERT Solutions
  • The Mughal Empire Question Answer Class 7 Social Science History Chapter 4 NCERT Solutions
  • India: Climate Vegetation and Wildlife Question Answer Class 6 Social Science Geography Chapter 8 NCERT Solutions
  • Traders, Kings and Pilgrims Question Answer Class 6 Social Science History Chapter 10 NCERT Solutions
  • Environment Question Answer Class 7 Social Science Geography Chapter 1 NCERT Solutions
  • Understanding Advertising Question Answer Class 7 Social Science Civics Chapter 7 NCERT Solutions
  • The Making of Regional Cultures Question Answer Class 7 Social Science History Chapter 9 NCERT Solutions

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions