NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.7 – Part 2

Formulas of cones: The base area of circle is=πr^2,and the volume is=1/3π r^2h

Understanding Cones and Slant Height

Formulas of cones: The base area of circle is=πr^2,and the volume is=1/3π r^2h

Q-3 The height of a cone is 15cm . If its volume is 1570cm3 , find the radius of the base. (Use π=3.14 )

Solution:

We are given,

  • Height (h) =15cm

  • Volume = 1570cm3

Consider, the radius of the base of cone to be rcm

Then, volume =13πr2h=1570cm3

  • 13πr2h=1570

  • 13×3.14×r2×15=1570

  • r2=1570×33.14×15

  • r2=15703.14×5

  • r2=100

  • r=10

Q-4 If the volume of a right circular cone of height 9cm is 48πcm3 , find the diameter of its base.

Solution:

Given,

  • Height (h)=9cm

  • Volume =48πcm3

Consider, the radius of the base of the cone be rcm

Now, volume =13πr2h=48πcm3

  • 13πr2h=48π

  • 13×r2×9=48

  • 3r2=48

  • r2=483

  • r2=16

  • r=4

Q-5 A conical pit of top diameter 3.5m is 12m deep. What is its capacity in kiloliters?

Solution:

Given,

  • Diameter of the top of the conical pit =3.5m therefore, radius (r)=(3.52)m=1.75m

  • Depth of the pit (h)=12m

Therefore, volume =13πr2h

  • =(13×227×1.75×1.75×12)m3

  • =38.5m3

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