Question

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

Answer 1

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