A pasta sauce can has a capacity of 725mL and a base radius of 4.2cm. The company plans to redesign the can with a larger base. The new can will have the same volume as the original can. A) let r represent the change in base radius. Let h centimetres represent the change in height. Write h as a function of r. B) what is the decrease in height for each increase in base radius? I) 0.5 cm ii)1.3cm. iii) 1.5 cm C) what is the increase in base radius for each decrease in height? i) 0.5cm ii)1.0cm iii) 1.5cm
Volume of cylinder = (area of circular base) x height
It's a 725 cm3 volume, so you can use the above formula to determine the can's height to be 13.08 cm
We are told that the new radius = 4.2 + r
So we can say the new height = 13.08 – h
So the formula for the volume of the new cylinder becomes
Pi • (4.2 + r)2 • (13.08 - h) = 725
Rearrange this to isolate h on one side by itself, and this is called expressing h as a function of r.
Now, substitute the various values of r to find the corresponding h.
Go back to the original formula and isolate r, and use this equation to answer the final questions.
Good luck! 🍀