21. A solid metallic cube of side 9 cm and a solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted to form a single cube. How much (in Rs.) is the cost to polish the new at a rate of Rs. 10 per cm2?
22. A wall 12 m long, 9 m high and 90 cm thick is to be constructed. Given that one pack contains 450 bricks, how many packs of bricks will be required if each brick is of dimensions 10 cm × 7.5 cm × 7 cm and the cement and sand mixture occupies one-eighteenth volume of the wall? (Rounded off to the nearest integer)
23. If a right circular cone is separated into solids of volumes V1, V2, V3 by two planes parallel to the base which also trisect the altitude, then V1 : V2 : V3 is
24. A sector of radius 10.5 cm with the central angle 120° is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in cm3) of the cone so formed?
25. A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is just completely submerged in water, then the rise of water level in the cylindrical vessel is:
26. A solid cube has side 8 cm. It is cut along diagonals of top face to get 4 equal parts. What is the total surface (in cm2) of each part?
27. The base of a right pyramid is a square of side 8√2 cm and each of its slant edge is of length 10 cm. What is the volume (in cm3) of the pyramid?
28. The base of a solid right prism of height 10 cm is a square and its volume is 160 m3. What is the total surface area of the prism (in cm2)?
29. A solid lead sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum number (in integer) of such spheres can be made?
30. A hemisphere is kept on top of a cube. Its front view is shown in the given figure. The total height of the figure is 21 cm. The ratio of curved surfaces area of hemisphere and total surface area of cube is 11 : 42. What is the total volume (in cm3) of figure?
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