### Mensuration Class 9th Mathematics Term 3 Tamilnadu Board Solution

##### Question 1.The length of the arc of a sector having central angle 90° and radius 7 cm isA. 22 cmB. 44 cmC. 11 cmD. 33 cmAnswer:Given:length of arc = ?radius = 7cmArc length =    ⇒ Arc length = 11cmOption (C) is correct.Question 2.If the radius and arc length of a sector are 17 cm and 27 cm respectively, then the perimeter isA. 16 cmB. 61 cmC. 32 cmD. 80 cmAnswer:Given:Perimeter = ?length of arc = 27cmradius = 17cmperimeter of sector = arc length + r + r= arc length + 2r= 2(17) + 27= 34 + 27 = 61cmOption (B) is correct.Question 3.If the angle subtended by the arc of a sector at the center is 90°, then the area of the sector in square units isA. 2πr2B. 4πr2C. D. Answer:Given:radius = rcentral angle = 90°Area of sector =   Option (C) is correct.Question 4.Area of a sector having radius 12 cm and arc length 21 cm isA. 126 cm2B. 252 cm2C. 33 cm2D. 45 cm2.Answer:Given:radius = 12cmarc length = 21cmArea of sector =  ⇒ area of sector = 126cmOption (A) is correct.Question 5.The area of a sector with radius 4 cm and central angle 60° isA. B. C. D. Answer:Given:radius = 4cmcentral angle = 60°Area of sector =    ⇒ central angle = 8π /3 cm2Option (C) is correct.Question 6.If the area and arc length of the sector of a circle are 60 cm2 and 20 cm respectively, then the diameter of the circle isA. 6 cmB. 12 cmC. 24 cmD. 36 cmAnswer:Given:area of sector = 60cm2arc length = 20cmArea of sector =  ⇒ Radius of circle = 6cmDiameter of circle = 12cmOption (B) is correct.Question 7.The perimeter of a sector of a circle is 37cm. If its radius is 7cm, then its arc length isA. 23 cmB. 5.29 cmC. 32 cmD. 259 cmAnswer:Given:Perimeter = 37cmradius = 7cmperimeter of sector = arc length + r + r= arc length + 2r37 = 2(7) + aa = 37 - 14 = 23cmOption (a) is correct.Question 8.A solid having six equal square faces is called aA. cubeB. cuboidC. squareD. rectangleAnswer:A solid having six equal square faces is Cube.Option (a) is correct.Question 9.The quantity of space occupied by a body is itsA. areaB. lengthC. volumeD. T.S.AAnswer:Quantity of space occupied by a body is its volume.Option (c) is correct.Question 10.The LSA of a cube of side 1dm isA. 16 dm2B. 4 dm2C. 2 dm2D. 1 dm2Answer:Given:side of cube (a) = 1dmLSA of cube = 4a2= 4(1)2= 4(1)⇒ LSA of cube = 4dm2Option (B) is correct.

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