Question

Answer this question using two different strategies. You have been asked to drill a hole into a metal cylinder to enable tubing to be inserted. The area of the resulting metal ring must comply to this formula: � = �(� + �)(� − �) where R is the radius of the outer cylinder and r is the radius of the inner hole. The radius of the metal cylinder is 21mm and the area of the resulting ring of metal after drilling must be no less than 9cm2 to remain stable and not bend. What size hole can you drill accurate to a hundredth?

Answer 1

Step-by-step explanation

We are given a formula for which the resulting metal must comply after drilling a hole to be:

`\begin{gathered} A=\pi(R+r)(R-r) \\ where \\ R\text{ is radius of the outer cylinder} \\ r\text{ is the radius of the inner hole} \end{gathered}`

We are also given some conditions

`\begin{gathered} A\ge9cm^2 \\ R=21mm \end{gathered}`

Our goal now will be to get the value of r