NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.7 – Part 3
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Cone Volume
Q-6 The volume of a right circular cone is. If the diameter of the base is, find
Height of the cone
Slant height of the cone
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 , than
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,