Question

A frustum is made by removing a small cone from a similar larger cone. Work out the volume of the frustum, Below

Answer 1

Answer:

732×pi cm³

Step-by-step explanation:

we have all the data and the formula.

so, we only need to do the raw calculations.

Vc = pi×r²×h/3

r = the radius of the basic circle

h = the height.

since the volume of the frustum is the volume of the large cone minus the volume of the small cone, we need to calculate both volumes and then subtract the smaller from the larger number.

oh, and we need to calculate also the radius of the base circle of the small cone. since they are similar bodies, all lines use the same ratio or scaling factor to convert from one cone to the other.

that includes height and radius.

we know the height of the large cone is 16+4=20 cm.

and set know that the height of the small cone is 16 cm.

so, the scaling factor is 16/20 = 4/5 to go from the large to the small cone.

that means that the radius of the small cone is

15 × 4/5 / 3×4 = 12 cm

so, now to the 2 cone volumes :

the large cone

Vcl = pi×15²×20/3 = pi×225×20/3 = pi×75×20 =

= pi×1500 cm³

the small cone

Vcs = pi×12²×16/3 = pi×144×16/3 = pi×48×16 =

= pi×768 cm³

the volume of the frustum is therefore

Vf = Vcl - Vcs = 1500×pi - 768×pi = 732×pi cm³