11. An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm. When a few solid spherical metallic balls each of radius $$\frac{1}{2}$$ cm are dropped in the vessel, 25% water is overflowed. The number of balls is:
12. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm. Find the volume of wooden toy (nearly)?
13. The base of right pyramid is an equilateral triangle, each side of which is 20 cm. Each slant edge is 30 cm. The vertical height (in cm) of the pyramid is:
14. The base, of a right prism is a regular hexagon of side 5 cm. If its height is 12√3 cm, then its volume (in cm3) is:
15. A hemispherical cup of radius 4 cm is filled to the brim with coffee. The coffee is then poured into a vertical cone of radius 8 cm and height 16 cm. The percentage of the volume of the cone that remains empty is:
16. The radius of the base of a cylinder is 14 cm and its volume is 6160 cm3. The curved surface area (in cm2) is: $$\left( {\pi = \frac{{22}}{7}} \right)$$
17. A solid metallic sphere of radius 15 cm is melted and recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of the original sphere and the sum of the surface areas of all balls?
18. Two solid right cones of equal height and of radii r1 and r2 are melted and made to form a solid sphere of radius R. Then the height of the cone is
19. The curved surface area of a right cylinder is 3696 cm2. Its height is three times its radius. What is the capacity (in liters) of the cylinder? $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
20. Water flows into a tank which is 200 m long and 150 m wide through a pipe of cross-section 0.3 m × 0.2 m at 20 km/hour. Then the time (in hours) for the water level in the tank to reach 8 m is
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