Question

Item 22 the navy pier ferris wheel in chicago has a circumference that is ​56% of the circumference of the first ferris wheel built in 1893. what was the radius of the first ferris wheel?

Answer 1

Given that the navy pier ferris wheel in chicago has a circumference of 439.6 ft that is  ​56% of the circumference of the first ferris wheel built in 1893.

Let x be the circumference of the first ferris wheel, the 56% of x = 439.6

0.56x = 439.6

x = 439.6 / 0.56 = 785 ft

Recall that the circumference of a circle is given by
$C=\pi r^2$

$785= \pi r^2 \\ \\ r^2= \frac{785}{ \pi } =249.87 \\ \\ r= \sqrt{249.87} =15.8 \ ft$

Therefore, the radius of the first ferris wheel is 15.8 ft.