NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.7 – Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Cone Volume

Q-6 The volume of a right circular cone is . If the diameter of the base is , find

  1. Height of the cone
  2. Slant height of the cone
  3. Curved surface area of the cone

Solution:

I. Diameter of the base of the cone

Therefore radius ()

Let the height of the cone be

  • Now, volume of the cone =

II. Radius , Height , Let the slant height of the cone be , then

III. Given,

  • Radius
  • Slant height

Therefore, curved surface area

Q-7 A right triangle with sides , and is revolved about the side . Find the volume of the solid so obtained.

Solution:

Note than when right triangle is revolved, we get a cone with the same radius as the base of the right triangle.

Cone Formed by Rotating Right Triangle
Triangle BEC

Height is .

In triangle

  • Base is
  • Height is .

Cone so obtained has radius r = 5 cm and height 12 cm. Its volume,