{"id":887,"date":"2020-09-15T04:48:06","date_gmt":"2020-09-14T23:18:06","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=887"},"modified":"2021-07-02T15:01:52","modified_gmt":"2021-07-02T09:31:52","slug":"kseeb-sslc-class-10-maths-solutions-chapter-5-ex-5-2","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-sslc-class-10-maths-solutions-chapter-5-ex-5-2\/","title":{"rendered":"KSEEB SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Ex 5.2"},"content":{"rendered":"

KSEEB SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Ex 5.2<\/strong> are part of KSEEB SSLC Class 10 Maths Solutions<\/a>. Here we have given Karnataka SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Exercise 5.2.<\/p>\n

Karnataka SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Exercise 5.2<\/h2>\n

{Unless stated otherwise, use \\(\\pi=\\frac{22}{7}\\)}<\/p>\n

Question 1.
\nFind the area of a sector of a circle with radius 6 cm if angle of the sector is 60\u00b0.
\nSolution:
\nRadius of a sector of a circle, r = 6 cm.
\nAngle of a sector of a circle, \u03b8 = 60\u00b0
\nArea of a sector of a circle = ?
\nArea of a sector of a circle \\(=\\frac{\\theta}{360} \\times \\pi r^{2}\\)
\n\"ex
\n= 18.8 sq.cm.<\/p>\n

Question 2.
\nFind the area of a quadrant of a circle whose circumference is 22 cm.
\nSolution:
\nCircumference of a circle, 2\u03c0r = 22 cm.
\nArea of a quadrant of a circle = ?
\n2\u03c0r = 22
\n\"KSEEB
\n\u2234 Area of a quadrant of a circle
\n\"KSEEB
\n\\(=\\frac{77}{8}\\)
\n= 9.62 sq. cm.<\/p>\n

Question 3.
\nThe length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
\nSolution:
\nLength of the minute hand of a clock, r = 14 cm.
\nArea swept by the minute hand in 5 minutes \\(=360 \\times \\frac{5}{60}\\)
\n= 30\u00b0
\nAngle of segment of a circle, 0 = 30\u00b0
\n\u2234 Area swept by the minute hand in 5 minute,
\n\"KSEEB<\/p>\n

Question 4.
\nA chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:
\n(i) minor segment, (ii) major sector. (Use \u03c0 = 3.14)
\nSolution:
\nRadius of the circle, r = 10 cm.
\nAngle at the centre of circle, \u03b8 = 90\u00b0
\n1) Area of minor segment = ?
\n2) Area of Major segment = ?
\n(i) Area of minor segment OAPB
\n\"KSEEB<\/p>\n

ii) Area of Minor Segment, APB :
\n= Area of OAPB – Area of AOAB
\n\\(=78.5 \\mathrm{cm}^{2} \\cdot-\\frac{1}{2} \\times \\mathrm{OA} \\times \\mathrm{OB}\\)
\n\\(=78.5-\\frac{1}{2} \\times 10 \\times 10\\)
\n= 78.5 – 50
\n= 28.5 sq. cm.<\/p>\n

(iii) Area of the Major Segment (AQBO):
\n\"KSEEB<\/p>\n

Question 5.
\nIn a circle of radius 21 cm, an arc subtends an angle of 60\u00b0 at the Centre. Find:
\n(i) the length of the arc,
\n(ii) area of the sector formed by the arc,
\n(iii) area of the segment formed by the corresponding chord.
\nSolution:
\nRadius of the circle, r = 21 cm.
\nAngle at the centre of the circle, \u03b8 = 60\u00b0
\n1) the length of the arc?
\n2) Area of the sector formed by the arc?
\n3) Area of the segment.
\n\"KSEEB
\n1) The length of arc OAPB
\n\"KSEEB
\n= 22 cm<\/p>\n

2) Area of the sector OAPB
\n\"KSEEB
\n= 231 sq. cm.<\/p>\n

3) Area of the segment APB:
\n= Area of the sector OAPB – Area of the equilateral \u2206OAB
\n\"KSEEB
\n= 231 – 190.7
\n= 40.3 sq. cm<\/p>\n

Question 6.
\nA chord of a circle of radius 15 cm subtends an angle of 60\u00b0 at the centre. Find the areas of the corresponding minor and major segments of the circle.
\n(Use \u03c0 = 3.14 and \\(\\sqrt{3}=1.73\\)).
\nSolution:
\nRadius of circle, r = 15 cm.
\nAngle at the centre, \u03b8 = 60\u00b0
\n1) Area of the minor segment =?
\n2) Area of the Major segment =?
\n\"KSEEB
\n(i) Area of Minor segment, APB :
\n= Area of sector OAPB – Area of \u2206OAB
\n\"KSEEB
\n= 117.75 sq. cm. – 97.31
\n= 20.44 sq. cm.<\/p>\n

ii) Area of the Major segment:
\n= Area of Circle – Area of a segment of circle OAPB
\n\"KSEEB
\n= 3.14 \u00d7 225 – 20.44
\n= 707.14 – 20.44
\n= 686.06 cm2.<\/p>\n

Question 7.
\nA chord of a circle of radius 12 cm subtends an angle of 120\u00b0 at the centre. Find the area of the corresponding segment of the circle.
\n(Use \u03c0 = 3.14 and \\(\\sqrt{3}=1.73\\)).
\nSolution:
\nRadius of the circle, r = 12 cm.
\nAngle at the centre, \u03b8 = 120\u00b0
\nArea of segment APB =?
\n(i) Area of sector OAPB:
\n\"KSEEB<\/p>\n

(ii) Area of segment APB:
\n\"KSEEB
\n\"KSEEB<\/p>\n

\u2234 Area of segment APB:
\n= Area of sector OAPB – Area of \u2206AOB
\n= 150.72 – 62.68
\n= 88.44 sq. cm.<\/p>\n

Question 8.
\nA 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 Figure). Find
\ni) the area of that part of the field in which the horse can graze.
\nii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (use \u03c0 = 3.14)
\n\"KSEEB
\nSolution:
\nLength of the rope, r = 5 m, \u03b8 = 90\u00b0
\nArea of segment =?
\n\"KSEEB<\/p>\n

(ii) Length of the rope, r = 10 cm, \u03b8 = 90\u00b0
\nArea of segment =?
\n\"KSEEB
\n\u2234 Area of the field which is increased in the grazing
\n= Equation (2) – Equation (1)
\n= 78.5 – 19.63
\n= 58.87 sq. cm.<\/p>\n

Question 9.
\nA brooch is made with silver wire in the form of a circle with a diameter of 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the Figure. Find
\ni) the total length of the silver wire required,
\nii) the area of each sector of the brooch.
\n\"KSEEB
\nSolution:
\nDiameter, d = 35mm \u03b8 = \\(\\frac{360^{\\circ}}{10}\\) = 36\u00b0
\nRadius, r = \\(\\frac{35}{2}\\) mm
\n(i) Length of the silver wire required :
\nLength of the wire used in making 5 diameter + Circumference of Silver, wire required.
\n\"KSEEB<\/p>\n

(ii) Area of each sector of the brooch = ?
\nDiameter of the brooch, d = 35mm
\nRadius, r = \\(\\frac{35}{2}\\) mm
\nAngle at the centre, \u03b8 = \\(\\frac{360^{\\circ}}{10}\\) = 36\u00b0
\nThe Area of each sector of the Brooch:
\n\"KSEEB<\/p>\n

Question 10.
\nAn umbrella has 8 ribs which are equally spaced (see the figure). Assuming the umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
\n\"KSEEB
\nSolution:
\nRadius of circle, r = 45 cm.
\nAngle at the centre, \u03b8 = \\(\\frac{360^{\\circ}}{8}\\) = 45\u00b0
\nArea between the two consecutive ribs of the umbrella =?
\nArea of each segment of the circle,
\n\"KSEEB<\/p>\n

Question 11.
\nA car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115\u00b0. Find the total area cleaned at each sweep of the blades.
\nSolution:
\nRadius of the wiper of the car, r = 25 cm.
\nAngle at the centre, \u03b8 = 115\u00b0
\nArea of the sector =?
\nArea of the blade when it is swept once
\n\"KSEEB
\nArea of two blades when swept:
\n\"KSEEB<\/p>\n

Question 12.
\nTo warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80\u00b0 to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (use \u03c0 = 3.14)
\nSolution:
\nRadius, r = 16.5 km. = \\(\\frac{33}{2}\\) km.
\nAngle, \u03b8 = 80\u00b0
\nArea of the Sector =?
\nArea of the sea over which the ships are warned
\n\"KSEEB<\/p>\n

Question 13.
\nA round table cover has six equal designs as shown in Figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm2<\/sup>.
\n(Use \\(\\sqrt{3}=\\) = 1.7)
\n\"KSEEB
\nSolution:
\nEach angle at the centre,
\n\"KSEEB
\n\"KSEEB
\nArea of segment APB design 1 :
\n= Area of OAPB – Area of \u2206AOB
\n= 410.6 – 333.2
\n= 77.46 sq.cm.
\n\u2234 Total are of SIX designs = 6 \u00d7 77.46
\n= 464.8 sq.cm.
\nCost of designing for 1 sq.cm, is Rs. 0.35
\n\u2234 Cost of designing for 464.8 sq.cm ………….
\n= 464.8 \u00d7 0.35
\n= Rs. 162.68<\/p>\n

Question 14.
\nTick the correct answer in the following:
\nArea of a sector of angle p (in degrees) of a circle with radius R is
\n\"KSEEB
\nSolution:
\nD) \\(\\frac{p}{720}\\) \u00d7 2\u03c0R2<\/sup><\/p>\n

We hope the given KSEEB SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Ex 5.2 will help you. If you have any query regarding Karnataka SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Exercise 5.2, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"

KSEEB SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Ex 5.2 are part of KSEEB SSLC Class 10 Maths Solutions. Here we have given Karnataka SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Exercise 5.2. Karnataka SSLC Class 10 Maths Solutions Chapter 5 Areas Related to Circles Exercise 5.2 …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/887"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=887"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/887\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}