1.

The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to its base. If the volume of a small cone is `1/64` of the volume of the given cone, at what height above the base is the section made?

Answer» `h/H = r/R = l/L`
volume of small cone= `1/3 pi r^2 h`
volume of bigger cone =`1/3 pi R^2 H`
Now, `1/3 pi R^2 H xx 1/64 = 1/3 pi r^2 h`
`(r^2H)/64 = r^2 h`
`h/40 = r/R`
`r= (hR)/40`
now, `(R^2H)/64 = (hR/40)^2 xx h`
`r^2 xx 40/64 = h^2R^2/(40)^2 xx h`
`h^3 = (40)^3/64`
`h= 40/4 = 10cm`
from the height 30cm from base of cone, the section made
Ans`h=10cm`
Answer


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