NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.7 – Part 3
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
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Height of the cone
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Slant height of the cone
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Curved surface area of the cone
Solution:
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Diameter of the base of the cone
Therefore radius ()
Let the height of the cone be
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Now, volume of the cone =
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Radius
Height
Let the slant height of the cone be , than
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Given,
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Radius
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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
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
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Base is
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Height is.
Cone so obtained has radius r = 5 cm and height 12 cm. Its volume,