NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.3 – Part 1

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Q-1 Diameter of the base of a cone is Equation and its slant height is Equation . Find its curved surface area.Solution:

Lateral and total surface area of the cone

Area of Cone

Lateral and total surface area of the cone

Cone has a slant height s which is given as Equation (because of Pythagoras theorem).

Here, cone radius (r) Equation and slant height (l) Equation . Therefore, curved surface area of the cone

  • = Equation

  • = Equation

  • = Equation

Q-2 Find the total surface area of a cone, if its slant height is Equation and diameter of its base is Equation .Solution:

  • Radius (r) Equation

  • Slant height (l) Equation

Total surface area of the cone

  • Equation

  • Equation

  • Equation

  • Equation

Q-3 Curved surface area of a cone is Equation and its slant height is Equation . Find

  1. Radius of the base and

  2. Total surface area of the cone.

Solution:

Solution (I)

Curved surface of a cone Equation and slant height (l) Equation

Therefore, Equation

  • Equation

  • Equation

  • Equation

  • Equation

Solution (II)

Therefore, total surface area of the cone

  • Equation

  • Equation

  • Equation

  • Equation

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