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maths important question for class tenth

61. If a line is drawn parallel to one side of a triangle, prove that the other two sides are divided in the same ratio. Using the above result, find AB when in ∆ABC , DE ║ BC so that AD = 2.4 cm , AE = 3.2 cm and EC = 4.8 cm.(6 cm)
62. In a triangle, if square of one side is equal to the sum of the squares of other two sides, then angle opposite the first side is a right angle.using the converse of above theorem determines the length of an altitude of an equilateral triangle of side 2a.(√3a)
63. The ratio of areas of similar triangles is equal to the ratio of the squares on the corresponding sides. Prove.Using the above theorem, prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on the diagonal. 
64. If the radii of the ends of a bucket 45cm high are 28cm and 7cm.Find its capacity and surface area.(48510 cm3 , 5461.5 cm2)
65. A bucket is in the form of a frustum of a cone and holes 28.490 litres of water. The radii of the top and bottom are 28cm and 21cm respectively. Find the height of the bucket.(15 cm)
66. A spherical cannon ball, 28cm in diameter is melted and cast into a right circular conical mould, the base of which is 35cm in diameter. Find the height of the cone.(40)
67. A toy is in the form of a cone mounted on a hemisphere of radius 7cm. The total height of the toy is 9.5cm. Find the total surface area and the volume of the toy. (470.8 , 847cm3)
68. A spherical shell of lead, whose external diameter is 18cm, is melted and recast into a right circular cylinder, whose height is 8cm and diameter 12cm. Determine the internal diameter of the shell. (4 cm)
69. A metallic right circular cone 20cm height and whose vertical angle are 60 is cut into two part at the middle of its height by a plane parallel to its base. if the frustum so obtained is drawn into a wire of diameter cm, find the length of the wire.(7964.4 m3)
70. Water in a canal, 30 dm wide and 12 dm deep is flowing with a velocity of 10 km/h. How much area will it irrigate in 30 minutes, if 4 cm of standing water is required for irrigation?(450000m3)
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