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mathematics imp. questions with answer

51. The lengths of two cylinders are in the ratio 3:1 and their diameters are in the ratio 1:2 .Calculate the ratio of their volumes.(3:4)
52. Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a number of 3 or 7?(2/5)
53. Find the least number of coins of diameter 2.5 cm and height 3 mm which are to be melted to form a solid cylinder of radius 3 cm and height 5 cm.(96)
54. The radii of two cylinders are in the ratio 2:3 and their heights are in 5:3. Calculate the ratio of their volume.(20/81)
55. The volume of two spheres are in the ratio 64 : 27. Find their radii if the sum of their radii is 21cm.the height of a cylinder is 15 cm. the curved surface area is 660 cm². find the radius .(7 cm)
56. The circumference of the edge f a hemispherical bowl is 132 cm. find the capacity of the bowl.(19404 cm3)
57. An electric pole is 10 m high. If its shadow is 10√3 m in length. Find the elevation of the sun.(30)
58. The largest cube is carved out of a cube of radius 7 cm. find the volume of the sphere.(1437.3 cm3)
59. A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the capacity of the vessel.(27020.6cm3)
60. Prove that the ratio of the areas of similar triangles is equal to the ratio of the squares on the corresponding sides.Using the above result, prove that “ if the areas of two similar triangles are equal , they are congruent”.
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