CBSE Class 10-Mathematics: Chapter – 13 Surface Areas and Volumes Part 19 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 14:

A metallic right circular cone high and whose vertical angle is is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter , find the length of the wire.

A Metallic Right Circular Cone


Diameter of the wire

Radius of the wire

Let the length of the wire be .

Then, Volume of the wire

According to the question,

Question 15:

The diameter of metallic sphere in . The sphere in melted and drawn into a wire of uniform cross section. If the length of wire is , find its radius.


Diameter of sphere


Let be radius of wire Volume of wire

Question 16:

Water flows at the rate of metre per minute through a cylindrical pipe having its diameter at . How much time will it take to fill a conical vessel where diameter of base is and depth ?


We have volume of the water that flows out in one minute

Volume of cylinder of diameter and length .

Volume of cylinder

Volume of conical vessel

Suppose the conical vessel is filled in minutes

Volume of the water flows out in minutes

Volume of conical vessel