Math, asked by alekya5660, 1 year ago

The height of a cone is 60cm. a small cone is cut off at the top by a plane parallel to the base and its volume is 1/64the voiume of original cone. find the height from the base at which the section is made .

Answers

Answered by ManushkasinghM
2
Height of original cone = 60 cm
Let the radius of the original cone of original cone be r₁.
Let the radius of the smaller cone be r₂.
Let the height of the smaller cone be h.
By similarity criterion,
r₁ / r₂ = h / 60

1 / 64 Volume of the original cone = Volume of the small cone
1 / 64 X 1 /3 π r₁² 60 = 1 / 3 π r₂² h 
1 / 64 X r₁² 60 = r₂² h
( r₁ / r₂ )² X h = 64 / 60
( h / 60 )² X h = 64 / 60
h³ / 3600 = 64 / 60
h³ = 64 X 60 
h = ∛ 3840
h = 64 ∛60
h = 15.659 cm
Therefore, the height of the smaller cone is 15.659 cm.
Hope this helps.





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