31. The height of a solid cylinder in 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm2) of the remaining solid?
32. The internal measure of a cuboidal room are with length as 12 m, breadth as 8 m and height as 10 m. The total cost (in Rs.) of white washing all four walls of the room and also the ceiling of the room, if the cost of white washing is Rs. 25 per m2 is:
33. If the radius of a sphere is increased by 4 cm, its surface area is increased by 464π cm2. What is the volume (in cm3) of the original sphere?
34. Which of the following two will provide more volume?
I. A cuboid of edges 6 cm, 7 cm and 8 cm
II. A cube of edge 7 cm
I. A cuboid of edges 6 cm, 7 cm and 8 cm
II. A cube of edge 7 cm
35. The curved surface area of a right circular cone is 2310 cm2 and its radius is 21 cm. If its radius is increased by 100% and height is reduced by 50%, then its capacity (in litres) will be (correct to one decimal place): $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
36. A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?
37. Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long 44 m wide. The time taken (in hours) for the rise in the level of water in the tank to be 7 cm is
38. The areas of three adjacent faces of a cuboidal tank are 3 m2, 12 m2 and 16 m2. The capacity of the tank, in litres is:
39. If a cuboid of dimensions 32 cm × 12 cm × 9 cm is cut into two cubes of same size, what will be the ratio of the surface area of the cuboid to the total surface area of the two cubes?
40. A sector is formed by opening out a cone of base radius 8 cm and heigh 6 cm. Then the radius of the sector is (in cm).
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