# NCERT Mathematics Class 10 Exemplar Ch 12 Surface Areas and Volumes Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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11.16 glass spheres each of radius are packed into a cuboidal box of internal dimensions and then the box is filled with water. Find the volume of water filled in the box.

Answer:

12. A milk container of height is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as and respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.

Answer: ₹

13. A cylindrical bucket of height and base radius is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is , find the radius and slant height of the heap.

Answer: ,

14. A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are and , respectively. If the slant height of the conical portion is 5 cm, find the total surface area and volume of the rocket

Answer: ,

15. A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?

Answer:

16. A hemispherical bowl of internal radius is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius and height . How many bottles are needed to empty the bowl?

Answer: 54

17. A solid right circular cone of height and radius is placed in a right circular cylinder full of water of height such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

Answer:

18. Water flows through a cylindrical pipe, whose inner radius is , at the rate of an empty cylindrical tank, the radius of whose base is . What is the rise of water level in tank in half an hour?

Answer:

19. The rain water from a roof of dimensions drains into a cylindrical vessel having diameter of base and height . If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.

Answer:

20. A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid is , and . The radius of each of the conical depressions is and the depth are . The edge of the cubical depression is . Find the volume of the wood in the entire stand.

Answer: