Question

Cone cut to parallel to base and ratio of volume is 1/27

Answer 1

When a cone is cut with a plane parallel to its base, it gives us two pieces.

I assume the ratio of the two pieces is  1 : 27.

One is a smaller cone on top of the previous cone. The other part is called a frustum.

Let the height of the top part (smaller cone) = h  
     its radius (base) = r.
     its volume = π/3 r² h

Height of frustum = H - h.
Height of the original big cone = H
    its base radius (bigger base of frustum) = R.
    its volume = π/3 R² H - π/3 r² h

We know that (by similar triangles principles)
     r : R = h : H
     h = H r / R

Ratio of volumes
1 : 27  = r² h : (R² H - r² h)
1/27  = r² H r / R :  (R² H - r² H r / R)
1/27  =  r³ :  (R³ - r³)

So   27 r³  =  (R³ - r³)
        28 r³  = R³
        r/R =  ∛28.

Same way    h/H = ∛28

Answer 2

Step-by-step explanation:

worst worst worst worst