NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.7 – Part 1

  • Previous

volume of cone=1/3 πr^2 h

Volume of Cone

volume of cone=1/3 πr^2 h

Relation between the height, radius and slant height of a cone.

Slant Height Radius and Height of Cone

Relation between the height, radius and slant height of a cone.

By the Pythagoras theorem, Equation

Q-1 Find the volume of the right circular cone with

  1. Radius Equation , height Equation

  2. Radius Equation , height Equation

Solution:

  1. Radius Equation

    Height Equation

    Therefore, volume of the cone

    • Equation

    • Equation

    • Equation

  2. Radius Equation Height Equation

Volume of the cone

  • Equation

  • Equation

  • Equation

Q-2 Find the capacity in liters of a conical vessel with

  1. Radius Equation , slant height Equation

  2. Height Equation , slant height Equation

Solution:

  1. Radius Equation Slant height Equation

    Consider the height of the conical vessel Equation . Then by applying Pythagoras theorem,

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

    Now, volume of the cone

    • Equation

    • Equation

    • Equation

    Therefore, capacity of the vessel Equation

  2. Height Equation Slant height Equation

    Consider the radius of the conical vessel Equation . Again using Pythagoras theorem,

  • Equation

  • Equation

  • Equation

  • Equation

  • Equation

Volume of the cone

  • Equation

  • Equation

  • Equation

Therefore, capacity of the vessel Equation , Equation

Explore Solutions for Mathematics

Sign In