Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 8.0 centimeters and the radius of the larger wheel is 19.7 centimeters. Through how many degrees will the larger wheel rotate if the smaller one rotates 91○?Answer choices are a) 36.95○b) 38.95○c) 36.85○d) 37.95○* All I did was that I got the circumference using c2 pi r, and I got the area using a pi r ^2, I did this for both wheels, but I am unsure what to do afterwards*.
pretty sure you just need to find out the circumference of each and then find out how much distance you are covering through 91 degrees of the first wheel, then find out what percent of the total difference that is in the large wheel, then multiply that percent by 360 to get the answer 39.4pi 123.7787 larger wheel circ. 16pi 50.26548 smaller wheel circ multiply by (91/360) 12.70599 distance covered by both wheels 12.70599/123.7787 10.265% (percent of larger wheel covered) multiply by 360 36.9543 A is the right answer
I got A, 36.95. The first wheel rotates 91 degrees. How much of its circumference moved? Well let's find the arc length. L 8(91/180)pi 12.706 cm We we went around 12.706 cm. Notice that both circles went around this much. So at what angle on the other wheel is the arc length 12.706? Well the entire circumference of that wheel is (2*19.7pi) 123.7788 cm. 12.706/123.7788 0.1027. This means that the arc length we covered is 10.27% of the entire circumference of the wheel. We want the angle that creates that arc. So multiply that by 360 degrees: 360(0.1027) 36.95
RadiusSmall 8cm RadiusLarge 19.7cm RS.Circ 50.26548246 360Deg 1Deg 0.13962634cm RL.Circ 123.7787506 360Deg 1Deg 0.343829862cm Rotation of 90Deg of RS (50.26/360)*91 12.70599696cm 90Deg Rotation of 90Deg Small wheel in cm * Rotation of 1Deg on Large wheel in cm nDegrees of Large wheel 12.70599696 * 0.343829862 36.95431481Deg 36.95Deg The answer is a) 36.95Deg
