Question

the height of a cone is 20cm. a small come is cut off from top by a plane parallel to the base . if it's volume be 1/125 of the volume of the original cone , determine at what height above the base is the section made​

Answer 1

Answer:

16cm......

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Answer 2

Question :

The height of a cone is 20cm. a small come is cut off from top by a plane parallel to the base. if it's volume be 1/125 of the volume of the original cone , determine at what height above the base is the section made?

Answer :

Above 16 cm of height, the base section should be made.

Explanation :

In ∆ABC and ∆ADE,

∠A = ∠A ( common angle )

∠ABC = ∠ADE

∴ ∆ABC ~ ∆ADE ( by AA similarity )

∴ AB/AD = BC/DE ( corresponding sides of similar ∆s are proportional )

Let AB be h, BC = r1 and DE = r2

=> h/20 = r1/r2

It is given that volume of ∆ABC = 1/125 of volume of ∆ADE

=> 1/3π(r1)²h = 1/3π(r2)²h × 20 × 1/125

=> (r1/r2)² = 20/(125h)

=> (h/20)² = 20/(125h)

=> h³ = (20×20×20)/125

=> h³ = 64

=> h = ³√64

=> h = 4cm

AE = 20 cm

=> AE - 4 = height at which base section is made.

=> 20 - 16 = height at which base section is made.

∴ Above 16 cm of height, the base section should be made.