Answer:
V2 = V1 ( r2 / r1 )^2
Step-by-step explanation:
If the ice cream manufacturer wants to keep the height constant and only change the radius of the cone, you are essentially looking at a similar cone with different dimensions.
The volume (V) of a cone is given by the formula:
V= π r^2 (h/3)
In this case, the manufacturer wants to keep the height \( h \) constant, so the volume is directly proportional to the square of the radius \( r \).
If the initial cone has a radius of ( r_1 = 3.5 ) cm and a height of ( h = 9 ) cm, and the manufacturer wants to change the radius to a new value ( r_2 ), the volumes of the two cones will be in the ratio ((r_2/r_1)^2).
So, the formula for the new volume (V_2) in terms of the original volume (V_1) and the new radius (r_2) would be:
V2 = V1 ( r2 / r1 )^2
You can use this formula to calculate the new volume or the new radius based on the given information.
