Question

1. the first ferris wheel, designed by george ferris, was built in 1893 in paris, france. it had a diameter of 76 m. about how far would you travel in 8 turns of this wheel? 17. a 10 - speed bicycle tire has a diameter of 27 in. in highest gear, the tire rotates 3.4 times with each pedal turn. about how far does the bike travel, in this gear, with each pedal turn? 18. a can contains 3 tennis balls, tightly packed. each ball has a diameter of 2.5 in. how much greater is the circumference of the can than the height of the can? 19. two runners are to race one lap on a circular track. the radius to the inside lane is 50 m. the radius to the outside lane is 51 m. how much of a head start should the runner on the outside get?

Explanation:

Problem 16

Step1: Find wheel circumference

$C = \pi d = \pi \times 76$

Step2: Calculate total distance

$\text{Total distance} = 8 \times 76\pi = 608\pi \approx 608 \times 3.14 = 1909.12$

Problem 17

Step1: Find tire circumference

$C = \pi d = \pi \times 27$

Step2: Calculate distance per pedal turn

$\text{Distance} = 3.4 \times 27\pi = 91.8\pi \approx 91.8 \times 3.14 = 288.252$

Problem 18

Step1: Find can circumference

$C = \pi d = \pi \times 2.5 \approx 7.85$

Step2: Calculate can height

$\text{Height} = 3 \times 2.5 = 7.5$

Step3: Find difference

$\text{Difference} = 7.85 - 7.5 = 0.35$

Problem 19

Step1: Find inside lane circumference

$C_1 = 2\pi r_1 = 2\pi \times 50 = 100\pi$

Step2: Find outside lane circumference

$C_2 = 2\pi r_2 = 2\pi \times 51 = 102\pi$

Step3: Calculate head start

$\text{Head start} = C_2 - C_1 = 102\pi - 100\pi = 2\pi \approx 6.28$

Answer:

1. $\boldsymbol{1909.12}$ meters
2. $\boldsymbol{288.25}$ inches
3. $\boldsymbol{0.35}$ inches
4. $\boldsymbol{6.28}$ meters