41. The rain water from a roof 22 m × 20 m drains into a cylindrical vessel having a diameter of 2 m and height 3.5 m. If the vessel is just full, then the rainfall (in cm) is:
42. The base of a right prism is an equilateral triangle. If the lateral surface area and volume are 120 cm2, 40√3 cm3 respectively then the side of base of the prism is
43. A solid cube is cut into three cuboids of same volumes. What is the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed?
44. A ball of lead 4 cm in diameter is covered with gold. If the volume of the gold and lead are equal, then the thickness of gold (given $$\root 3 \of 2 $$ = 1.259) is approximately
45. A right triangle with sides 9 cm, 12 cm and 15 cm is rotated about the side of 9 cm to form a cone. The volume of the cone so formed is:
46. The volume of a right circular cone is 1232 cm3 and its vertical height is 24 cm. Its curved surface area is
47. The curved surface area of a cylinder is five time the area of its base. Find the ratio of radius and height of the cylinder.
48. A hollow cylindrical tube 20 cm long is made of iron and its external and internal diameters are 8 cm and 6 cm respectively. The volume of iron used in making the tube is $$\left( {\pi = \frac{{22}}{7}} \right)$$
49. A solid cone of height 9 cm with diameter of its base 18 cm is cut out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is:
50. If the number of vertices, edges and faces of a rectangular parallelopiped are denoted by v, e and f respectively, the value of (v - e + f) is
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