Question

A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 276ft long. The barrel has a circular base that turns 46 times in being rolled up the ramp. What is the diameter of the circular base?Use the value 3.14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.

Answer 1

Given

The length of a ramp is 276 ft .

The circular base barrel turns 46 times in being rolled up the ramp.

Step-by-step explanation

To find the diameter of the circular base.

The length covered by barrel is equal to the circumference of the circle .

Therefore, we can write as

`2\pi r=L`

Use the relation of diameter and radius to find the diameter.

`d=2r`

Substitute the value of radius to find the diameter.

`L=\pi d`

Also the number of times the barrel turns is 46 .

And the relation between number of times the barrel turns, length of barrel and length of ramp is

`\begin{gathered} 46=(276)/(\pi d) \\ d=(276)/(46*\pi) \end{gathered}`
`d=1.91ft`

Answer

Hence the diameter of the circular base is 1.91 ft.