Question

height of a cone is 30cm a small cone is cut off at the top by a plane parallel to the base if its volume be one hour. 27 of volume of the given cone at what height above the base is the section made
according to 5 marks question​

Answer 1

hope this is the right answer

Answer 2

HEYA MATE!!

Here's your answer!!

Mark the top vertex as A, half of the plane cutting the cone as DE and base radius as BC.

Let the height of the larger cone be h, let the height of the smaller cone be h₁, top radius of the frustum be r₂ and base radius of frustum be r₁.

In ΔABC and ΔADE,

∠ABC = ∠ADE = 90°

∠BAC = ∠DAE (common)

∴ ΔABC is similar to ΔADE (AA similarity)

=> AD/AB = DE/BC

=> h₁/h = r₂/r₁

=> h₁/30 = r₂/r₁

=> h₁ = (30 × r₂)/r₁

Volume of small cone = 1/ 27 × Volume of big cone

=> 1/3 π × r₂² × h₁ = 1/27 × 1/3 π × r₁ × h

=> r₂² × h₁ × 27 = r₁² × h₁

=> r₂²  × [(30 × r₂)/r₁] × 27 = r₁² × 30

=> r₁² = (r₂² × r₂ × 27) / r₁

=> r₁³/ r₂³ = 27

=> r₂³/ r₁³ = 1 / 27

=> r₂/r₁ = 1 / 3

Therefore,

h₁/h = 1 / 3

=> h₁/ 30 = 1 / 3

=> h₁ = 10 cm

Hope this helps you!!

Cheers :D

#foreverJungkook