Question

The slant height of a right circular cone is 10 cm and its height is 8 cm. It is cut by a plane parallel to its base passing through the midpoint of the height. Find the ratio of the volume of the cone to that of the frustum of the cone

Answer 1

Answer:

8/7

Step-by-step explanation:

See the attached  picture for problem description.

Given: OE = 8 cm

OF = 4 cm  

OB = 10 cm

BE²=OB²−OE²

= 100 – 64 = 36

 

Therefore, BE = 6.

Then FC = 3 (F is mid point of OE)

Volume of cone OAB = πr²h/3 (here r = EB, h = OE)

= π * 6 *6 *8/3

= 96π

Volume of cone OCD (r = FC, h = OF)

=π*3*3×4/3  

=12π

Volume of frustum ABCD = 96π−12π = 84π

Ratio of total cone to Frustum = Volume of Cone / Volume of Frustum

= 96π / 84π

= 8/7