Answer to Question #194455 in Geometry for Andu

Question

The diameter of the "London Eye" carousel is 135 m. It has 32 bins to sit on, equidistant from each other along its contour. It takes 30 minutes to complete one rotation. Can you find the length of the arch between two adjacent bins? How long does a basket go in 10 minutes?

Answer 1

Explanations & Calculations

• When 32 bins are set up around the carousel, you can see there exist altogether 32 gaps\archs around it.
• This happens due to the shape of the carousel being a circle.
• This is the key point you need to figure out to work out this sum then the rest is easy.

• The circumference of the carousel is

$\qquad\qquad \begin{aligned} \small C&=\small 2\pi r=\pi(2r)=\pi d\\ &=\small \pi \times 135\,m\\ &=\small 424.12\,m \end{aligned}$

• Then the length of one arch is

$\qquad\qquad \begin{aligned} \small L&=\small \frac{C}{32}=\frac{424.12\,m}{32}\\ &=\small \bold{13.25\,m} \end{aligned}$

• Then for the latter part, we can rely on ratios.
• s mentioned, a single bin takes 30 minutes to complete a round, then let's take it travels some x distance over 10 minutes.
• Then the ratios be like

$\qquad\qquad \begin{aligned} \small \frac{C}{30}&=\small \frac{x}{10} \end{aligned}$

• Then we can simply get the required answer.

$\qquad\qquad \begin{aligned} \small x&=\small 10\times\frac{424.12}{30}\\ &=\small \bold{141.37\,m} \end{aligned}$