Question

A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.

answer is

Volume of the whole cone = 1/3 x 22/7 x 8² x 12 = 804.57  cm³

Radius, r, of small cone is found by similarity:
8/12 = r/6
r = 4cm

Volume of the small cone cut off = 1/3 x 22/7 x 4² x 6 = 100 4/7
 Volume of frustum = 804.57 - 100.57 = 704 cm³

The ratio of the two volumes = 100 4/7 : 704 = 1: 7

But in following line how the answer is 100 4/7

Volume of the small cone cut off = 1/3 x 22/7 x 4² x 6 = 100 4/7

Please help urgently

Answer 1

Radius of small cone=4cm...Applying similarity.

Ratio of cone volume/Ratio of frustum volume=1:7