Question

two wheels are rolled simultaneously. The radius of the smaller wheel is r feet and the radius of the larger wheel 2r feet. If both wheels did a total of 4 rotations, how much further did the large wheel travel? PLEASE SHOW STEPS TYSM

Answer 1

The circumference of a circle is C=2πR, where R is the radius of the circle and π≈3.14.

So if we open the circumference of the circle into a straight line segment, the length of this segment is C=2πR≈2*3.14*R=6.28R

4 rotations mean 4 circumferences that is 4 segments of length 6.28R,
which makes a linear distance of 4*6.28R=25.12R


i: the radius of the smaller wheel is R=r, thus it covers a distance of 25.12r feet

ii: the radius of the smaller wheel is R=2r, thus it covers a distance of 25.12*2r=50.24r (feet)

50.24r is twice 25.12r, thus the larger wheel traveled Twice the distance of the smaller one.


Answer: the larger covered twice the distance of the smaller.