NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.7 – Part 3

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Cone volume=1/3 πr^2 h

Cone Volume

Cone volume=1/3 πr^2 h

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:

  1. Diameter of the base of the cone

    Therefore radius ( )

    Let the height of the cone be

    • Now, volume of the cone =

  2. Radius

    Height

    Let the slant height of the cone be , than

  3. 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.

When a right triangle is rotated its base becomes the radius of the resulting code and height is shared.

Cone Formed by Rotating Right Triangle

When a right triangle is rotated its base becomes the radius of the resulting code and height is shared.

Triangle BEC

Triangle BEC has radius 5cm, and height 12cm

Height is .

In triangle

  • Base is

  • Height is .

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