31. From a solid cylindrical wooden block of height 18 cm and radius 7.5 cm, a conical cavity of the same height and same radius is taken out. What is total surface area (in cm2) of the remaining solid?
32. The volume of a cylinder is 4312 cm3. Its curved surface area is one-third of its total surface area. Its curved surface area (in cm2) is: $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
33. A right triangular pyramid XYZB is cut from cube as shown in figure. The side of cube is 16 cm. X, Y and Z are mid points of the edges of the cube. What is the total surface area (in cm2) of the pyramid?
34. A spherical ball of radius 1 cm is dropped into a conical vessel of radius 3 cm and slant height 6 cm. The volume of water (in cm3), that can just immerse the ball, is
35. If the radius of the base of a cone is doubled, and the volume of the new cone is three times the volume of the original cone, then what will be the ratio of the height of the original cone to that of the new cone?
36. The volume of a hemisphere is $$2425\frac{1}{2}$$ cm3, Find the radius. $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
37. The sum of length, breadth and height of a cuboid is 20 cm. If the length of the diagonal is 12 cm, then find the total surface area of cuboid.
38. If the radii of the circular ends of a frustum which is 45 cm high be 28 cm and 7 cm then the capacity of the bucket in cubic centimetre is. $$\left( {{\text{Use }}\pi = \frac{{22}}{7}} \right)$$
39. The length of the side of a cube is 2.8 cm. What is the volume of the largest sphere that can be taken out of the cube?
40. A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in cm2) of all the 8 parts?
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