class lX Surface area and Volume (part 2)

 Volume of a Cuboid = base area × height = length × breadth × height

Volume of a Cube = edge × edge × edge = a ³

Volume of a Cylinder = πr ²h

Volume of a Cone = 1/3 πr ²h

Volume of a Sphere = 4/ 3 3 πr³

Volume of a Hemisphere = 2/3 3 πr³

IMPORTANT QUESTIONS

1. Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the (i) radius r′ of the new sphere, (ii) ratio of S and S′.

2. The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

3. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³ ) is needed to fill this capsule?

4. A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

5. A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

6. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

7. The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

8. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³ of wood has a mass of 0.6 g.

9. At a Ramzan Mela, a stall keeper in one of the food stalls has a large cylindrical vessel of base radius 15 cm filled up to a height of 32 cm with orange juice. The juice is filled in small cylindrical glasses  of radius 3 cm up to a height of 8 cm, and sold for Rs.15 each. How much money does the stall keeper receive by selling the juice completely?

10. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas. 

11. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

12. The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

13. A godown measures 40 m × 25 m × 15 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.