Question

A hula hoop has a radius of 19 inches. what is the length of the arc subtending 1/4 of the hoop?

A. 43.8
B. 14.9
C. 29.8
D. 59.7

Answer 1

C. 29.8 inches

Explanation:

Length of complete hula hoop(L)= circumference of hoop

=>
`L=2\pi r`

where radius, r= 19 inches

Therefore length of arc(l) subtending 1/4 of the hoop is

=>
`l=(1)/(4)* L=(1)/(4)*2\pi r=(\pi r)/(2)`

=>
`l=(\pi * 19)/(2)inches=29.8 inches`

Thus the length of the arc subtending 1/4 of the hoop is 29.8 inches

Answer 2

Find the circumference:

Circumference = 2 x PI x radius

Circumference = 2 x 3.14 x 19 = 119.32

Divide by 4: 119.32 / 4 = 29.83 rounded to 29.8

The answer is C.