The height of a cone is 120 cm a small

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the height of the cone is 120 CM a small cone is off at the top by a plane parallel to the base and volume is 1/64 the volume of the original cone the height the base at which the section is made is​

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Answer : 90cm from the base of which the section is made.

height of the cone , h = 120cm

Let a small cone is cut off at the top by a plane parallel to the base.

length of small cone is l and radius of small cone is x.

a/c to question,

volume of small cone = 1/64 × volume of original cone

or, 1/3 πx²l = 1/64 × πR²h

or, x²l = 1/64 × R² × 120

or, x²l = 15R²/8 ..........(1)

see figure, from ∆ABC and ∆AED

\angle{ABC}=\angle{AED} [corresponding angles ]

\angle{ACB}=\angle{ADE} [ corresponding angles ]

so, \Delta ABC\sim\Delta AED

\therefore\frac{AC}{AD}=\frac{CB}{DE}

\frac{l}{h}=\frac{x}{R}

or, lR = hx = 120x

or, l = 120x/R .......(2)

from equations (1) and (2),

x² × (120x/R) = 15R²/8

or, 120x³ = 15R³/8

or, 64x³ = R³

or, x/R = 1/4

hence, x = R/4 , put it in equation (2),

l = 120 × (R/4)/R = 30cm

hence, (120cm - 30cm) = 90cm from the base of which the section is made.

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