A cone has a radius of 40 cm and a volume of 1875. what is the volume of a similar cone with a radius of 16 cm

The volume of a cone by definition is given by:

V = (pi * r ^ 2 * h) / (3)

Where,

r: radio

h: height

Clearing the height of the original cone we have:

h = (3 * V) / (pi * r ^ 2)

Substituting values:

h = (3 * 1875) / (pi * (40) ^ 2)

h = 1.119058194

We now look for the scale factor:

K = 16/40

Simplifying:

K = 4/10

K = 2/5

We apply the scale factor to the new volume:

V ' = ((k ^ 3) * (pi * r ^ 2 * h)) / (3)

Substituting:

V ' = (((2/5) ^ 3) * (pi * (16) ^ 2 * (1.119058194))) / (3)

V ' = 19.2 cm ^ 3

Answer:

the volume of a similar cone with a radius of 16 cm is:

V ' = 19.2 cm ^ 3