21. The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is $$\frac{1}{6}$$ the radius of the large sphere. What is the sum (in cm2) of curved surface areas of small spheres?
22. The perimeter of the triangular base of a right prism is 15 cm and radius of the in circle of the triangular base is 3 cm. If the volume of the prism be 270 cm3, then the height of the prism is
23. 40 men took a dip in a pool 30 m long and 25 m broad. If the average water displaced by a man is 5 m3, then what will be the rise (in cm) in level of the pool?
24. The ratio of the of two cones is 5 : 6 and their volumes are in the ratio 8 : 9. The ratio of their height is:
25. A 15 m deep well with radius 2.8 m is dug and the earth taken out from it is spread evenly to from a platform of breadth 8 m and height 1.5 m. What will be the length of the platform? $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
26. A solid cylinder has total surface area of 462 sq. cm. Its curved surface area is one third of the total surface area. Then the radius of the cylinder is
27. The radius of the base and height of a right circular cone are in the ratio 5 : 12. If the volume of the cone is $$314\frac{2}{7}$$ cm3, the slant height (in cm) of the cone will be
28. If the sum of radius and height of a solid cylinder is 20 cm and its total surface area is 880 cm2 then its volume is
29. A right pyramid stands on a square base of diagonal 10√2 cm. If the height of the pyramid is 12 cm, the area (in cm2) of its slant surface is
30. N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is:
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