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
Accepted Solution
A:
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