A hotel is in the shape of a cylinder, with a circular foundation. The circumference of the foundation is 4 times the radius, increased by $109.44 \mathrm{ft}$. Find the radius of the circular foundation. Use 3.14 as an approximation for $\pi$.
The radius of the foundation is approximately (Simplify your answer. Type an integer or decirfal rounded to the nearest hundredth as needed.)
Answer
Final Answer: The radius of the foundation is \(\boxed{48}\) ft.
Step 1 ：The problem provides that the circumference of the foundation is 4 times the radius, increased by 109.44 ft. This can be represented by the equation \(2\pi r = 4r + 109.44\), where \(C = 2\pi r\) is the formula for the circumference of a circle and \(r\) is the radius.
Step 2 ：Solving this equation for \(r\) will give us the radius of the foundation.
Step 3 ：By simplifying the equation, we find that the radius \(r\) is approximately 48 ft.
Step 4 ：Final Answer: The radius of the foundation is \(\boxed{48}\) ft.
