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 9856cm3 . If the diameter of the base is 28cm , 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 =28cm

    Therefore radius (r)=282cm=14cm ( radius=diameter2 )

    Let the height of the cone be hcm

    • Now, volume of the cone = 13πr2h=9856cm3

    • 13πr2h=9856cm3

    • 13πr2h=9856

    • 13×227×14×14×h=9856

    • h=9856×3×722×14×14

    • h=48cm

  2. Radius (r)=14m

    Height (h)=48cm

    Let the slant height of the cone be l , than

    • l2=h2+r2

    • l2=482+142

    • l2=2304+196

    • l2=2500

    • l=2500

    • 50cm

  3. Given,

  • Radius (r)=14m

  • Slant height (l)=50cm

Therefore curved surface area =πrl

  • =(227×14×50)cm2

  • =2200cm2

Q-7 A right triangle BEC with sides 5cm , 12cm and 13cm is revolved about the side 12cm . 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 12cm .

In triangle BEC

  • Base is 5cm

  • Height is 12cm .

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

  • =13πr2h

  • =(13×π×5×5×12)cm3

  • =100πcm3

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