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

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 Equation . If the diameter of the base is Equation , 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 Equation

    Therefore radius Equation ( Equation )

    Let the height of the cone be Equation

    • Now, volume of the cone = Equation

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

  2. Radius Equation

    Height Equation

    Let the slant height of the cone be Equation , than

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

  3. Given,

  • Radius Equation

  • Slant height Equation

Therefore curved surface area Equation

  • Equation

  • Equation

Q-7 A right triangle Equation with sides Equation , Equation and Equation is revolved about the side Equation . 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 poly1 Triangle poly1: Polygon A, B, C Ellipse d Ellipse d: Ellipse with foci A, C passing through D Segment c Segment c: Segment [A, B] of Triangle poly1 Segment a Segment a: Segment [B, C] of Triangle poly1 Segment b Segment b: Segment [C, A] of Triangle poly1 Segment f Segment f: Segment [B, E] Point B B = (1.04, 4.72) Point B B = (1.04, 4.72) Point B B = (1.04, 4.72) Point C C = (3.12, 1.8) Point C C = (3.12, 1.8) Point C C = (3.12, 1.8) Point E Point E: Point on d Point E Point E: Point on d Point E Point E: Point on d 13cm text1 = "13cm" 12cm text2 = "12cm" 5cm text3 = "5cm"

Triangle BEC

Triangle BEC has radius 5cm, and height 12cm

Height is Equation .

In triangle Equation

  • Base is Equation

  • Height is Equation .

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

  • Equation

  • Equation

  • Equation

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