Question

A barrel shaped like a cylinder is laid on its side and rolled up a ramp. The barrel has a circular base that is
2.5 ft in diameter. If the barrel turns 26 times in being rolled up the ramp, how long is the ramp?
Use the value 3.14 for a. Round your answer to the nearest tenth. Do not round any intermediate steps.

Answer 1

Check the picture below.

if the barrel is rolled up the ramp 26 times, each time the barrel is rolled up fully, it covers a length the circumference of its base, so if it does it 26 times, it wen up its base circumference 26 times.

$\textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d=2.5 \end{cases}\implies C=2.5\pi \implies \stackrel{\textit{26 times}}{C =65\pi }\implies \stackrel{\pi =3.14}{C=204.1}$