Question

A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 136 m long. The barrel has a circular base that turns 34 times in being rolled up the ramp. What is the diameter of the circular base?

Answer 1

Explanation:

The circumference of the circular base of the barrel is equal to the distance it travels while rolling up the ramp, which is 136 meters. We can use the number of rotations (34) and the circumference to find the diameter of the base.

Let's call the diameter of the circular base "d".

The circumference of the base is equal to the distance traveled while rolling up the ramp, which is 136 meters:

C = 2 * π * r = 136

where r is the radius of the base.

Since the base rotates 34 times, the distance traveled is 34 times the circumference:

34 * C = 34 * 136

4,624 = 136 * 34

Solving for the radius:

r = 4,624 / (2 * π)

And finally, solving for the diameter:

d = 2 * r = 2 * 4,624 / (2 * π) = 928 / π

So, the diameter of the circular base of the barrel is approximately 295.3 cm, rounded to the nearest tenth.