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Exercise 24 - (b)

Q. 1. (a). The surface area of a sphere is 452(4/7) cm2. Find its volume. (Use π = 22/7).

1(b). The surface area of a solid metallic sphere is 616 cm². It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained ?

Q. 2. If the number of square centimeters on the surface of sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere ?

Q. 3. The volume of two spheres are in the ratio 27 : 64. Find the radii if the sum of their radii is 42 cm. 

Q. 4. A metallic sphere of density 2 gm per cubic cm is 42 cm in diameter. Can a person who can lift 90 kg, lift this sphere ? (Use π = 22/7).

Q. 5.The ratio of surface areas of two spheres is 16 : 9. Find the ratio of their volumes.

Q. 6. A sphere of radius r is divided into four identical parts. Find the total surface area of one part.

Q. 7. A solid metal sphere is cut through its centre into 2 equal parts. If the diameter of the sphere is 3.5 cm, find the total surface of each part correct to two decimal places. (Use π = 22/7).

Q. 8. A hollow spherical shell is made of a metal of density 4.9 gm/cm³. If its internal and external diameters are 10 cm and 12 cm respectively, find the weight of the shell. (Take π = 3.1416).

Q. 9. If three solid spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and formed into a single sphere, find the radius of the single sphere. (Use π= 22/7).

Q. 10. Eight metallic spheres, each of radius 2 mm are melted and cast into a single sphere. Calculate the radius of the new (single) sphere. (Use π = 22/7).

Q. 11. The diameter of a sphere is 14 cm, find its volume and surface area. (Use π = 22/7).

Q. 12. The volume of one sphere is 64 times that of another sphere . Calculate the ratio of their (i) radius and (ii) surface areas. (Use π = 22/7).

Q. 13. Find the volume of the sphere whose surface area is 1000 cm². (Use π = 22/7).

Q. 14. The circumference of the edge of a hemispherical bowl is 132 cm. Find the capacity of the bowl. (Use π = 22/7).

Q. 15. The internal and external diameter of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost of paint 1 cm² of the surface is Re.0.05. Find the total cost to paint the vessel all over. (Use π = 22/7).

Q. 16. Three solid balls of metal of radii 8 cm, 6 cm and r cm are melted to form a solid sphere of radius 9 cm. Find r. 

Q. 17. A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half of the radius of the original one. How many such balls can be made ?