NCERT Mathematics Class 10 Exemplar Ch 12 Surface Areas and Volumes Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. A solid metallic hemisphere of radius is melted and recasted into a right circular cone of base radius . Determine the height of the cone.


2. A rectangular water tank of base contains water upto a height of . If the water in the tank is transferred to a cylindrical tank of radius , find the height of the water level in the tank.


3. How many cubic centimetres of iron is required to construct an open box whose external dimensions are , and provided the thickness of the iron is . If one cubic cm of iron weighs find the weight of the box.

Answer: ,

4. The barrel of a fountain pen, cylindrical in shape, is long and in diameter. A full barrel of ink in the pen is used up on writing words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?

Answer: words

5. Water flows at the rate of minute through a cylindrical pipe in diameter. How long would it take to fill a conical vessel whose diameter at the base is and depth ?

Answer: 51 minutes 12 sec

6. A heap of rice is in the form of a cone of diameter and height . Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Answer: ,

7. A factory manufactures pencils daily. The pencils are cylindrical in shape each of length and circumference of base as . Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at ₹ .

Answer: ₹

8. Water is flowing at the rate of through a pipe of diameter into a cuboidal pond which is long and wide. In what time will the level of water in pond rise by ?

Answer: 2 hours

9. A solid iron cuboidal block of dimensions is recast into a hollow cylindrical pipe of internal radius and thickness . Find the length of the pipe.


10.500 persons are taking a dip into a cuboidal pond which is long and broad. What is the rise of water level in the pond, if the average displacement of the water by a person is ?