Mock Question Paper on Height and Distance for CLAT 2020
Mock Question Paper on Height and Distance for CLAT 2020
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Mock Question Paper on Height and Distance for CLAT 2020What is the maximum area that can be enclosed in a triangle with semi perimeter 12cm?Area of a circle is 81cm2. What is the area of sector whose corresponding arc subtends an angle 2(pi)/9 at the centre of the circle?What is the area of a triangle ABC, If AB = 12cm, BC = 14cm and Angle ABC = 30°?On walking 30m towards a pole from A to B, the angle of elevation of top of the pole changes from 30° to 45°. Find the height of the pole. A pool of diameter 25m is dug 15m deep. The mud taken out is uniformly spread around the pool to form an embankment 5m high. What will be the resulting width of embankment?An iron ball of diameter 7inches is dropped into a cup of diameter 1 feet filled with water. Find rise in water level of the cup.The inner radius of a hollow sphere is 7cm, while thickness of the material is 2cm. What is the volume of material used in sphere?A rectangular sheet of dimension 22cm*14cm is rolled in a cylinder. Find the radius of new cylinder.In the previous question, what will be the volume of the cylinder?What will be the curved surface area of cylinder (only sheet area) in question 8?Answer and Solutions:Ans: 163 cm2Sol: Given semi perimeter of a triangle, an equilateral triangle encloses maximum areaSide of equilateral triangle = 12*2/3 = 8cm Area (maximum) = 3 *8*8/ 4 = 16 3 cm2 Ans: 9cm2Sol: Area of the circle = (pi) R2= 81 R2 = 81/(pi)Area of the sector = 1 R2θ/2 = ½ * 81 / (pi) * 2(pi) /9 = 9 cm2Ans: 42cm2Sol: Area of triangle= ½ *product of two side * sine of including angleArea of triangle = ½ * 12 * 14 *1/2 = 42 cm2 Ans: 40.98cmSol: A triangle with pole as perpendicular (height) and base length from pole foot to point B be xTan 45° = h/x tan 30 ° = h/ x+30h=x … eq (1) 1/3 = h/h+30 h3 = h + 30h*(3 -1 ) = 30 => h = 30/(1.732-1) = 40.98cm Ans: 7.25cmSol: Volume of hollow cylindrical embankment = volume of mud taken out. (pi) (R2-r2) 15 = (pi) r2*5 (R2 – 12.52)15= 12.52 *10 R2 = 12.5*12.5*15/10 + 156.25 = 390.625 R= 19.75 => Embankment width = R-r = 19.75 – 12.5 =7.25 cm Ans: 1.58 inchesSol: Radius of Cup = ½ =0.5 feet = 6 inchesVolume of water rise [(pi)*R2*h] =Volume of iron ball (4/3 * (pi) * r3)(pi) 62* h = 4/3 * (pi) * 7*7*7/2*2*2 h= 7*7*7*4/6*6*3*8 = 1.58 inches Ans: 1617cm3Sol: Inner Radius, r = 7 cm; Outer Radius, R = 7+2cm = 9 cmVolume of material used= 4/3 * (pi) * (R3 –r3) = 4/3 *22/7 * (93 -73) = 1617.5 cm3Ans: 3.5cmSol: Circumference of the cylinder circular end = length of sheet = 22cm 2(pi) r = 22 => r = 22*7/2*22 = 3.5 cmAns: 539cm3Sol: Height of Cylinder = Breadth of cylinder = 14cmVolume of cylinder = (pi) * 14 *3.5*3.5 [as volume of cylinder=(pi)r2h] = 539cm3Ans: 308cm2 Sol: As the area of cylinder will be the same as sheet’s area hence curved surface area of the cylinder = 22*14 = 308cm2 (function( $ ) {
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Aditya Anand
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