Question

A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 5.9 long. The barrel has a circular base that is 0.5in diameter. How many times does the barrel turn in being rolled up the ramp?
Use the value 3.14 for Pi . Round your answer to the nearest tenth. Do not round any intermediate steps.
A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 5.9 long. The barrel has a circular base that is 0.5in diameter. How many times does the barrel turn in being rolled up the ramp?
Use the value 3.14 for Pi . Round your answer to the nearest tenth. Do not round any intermediate steps.
@Mathematics

Answer 1

Since we're measuring how many times the barrel is going to be turning, we need to know what its circumference is. The formula for the circumference of a circle is\[C=2\pi r.\]Thus,\[C=2\pi r=2\pi(0.25)=\frac{1}{2}\pi.\]I used 0.25 above because the diameter is 0.5 (and we're looking for the radius). Since we have a ramp that is 5.9-something long, we divide this number by the circumference of the circle:\[\frac{5.9}{\frac{1}{2}\pi}=\frac{11.8}{\pi}=3.75.\]Thus the barrel is going to roll almost 4 times (round that to the nearest tenth, as required).