the new radius be to meet the client's need is 4.9 cm .
Explanation:
Here we have , can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company's clients needs a cylindrical can that has the same volume but is 15 cm tall. We need to find What must the new radius be to meet the client's need . Let's find out:
Let we have two cylinders of volume
with parameters as follows :

We know that volume of cylinder is
, According to question volume of both cylinder is equal i.e
⇒

⇒

⇒

⇒

⇒
Putting all values
⇒

⇒

⇒

⇒

⇒

Therefore , the new radius be to meet the client's need is 4.9 cm .