# Word problem in Arcs

• Oct 27th 2012, 06:11 PM
M670
Word problem in Arcs
Find the distance that the earth travels in one day in its path around the sun. Assume that a year has 365 days and that the path of the earth around the sun is a circle of radius 93 million miles.

so if I take 365 days and divide it by 360 degrees the earth moves ruffly 1.01 degrees per day then S=rθ
93millionmiles times 1.01 but that doesn't make sense so if I take 1 degree which equal (pi/180) =.017 as my theta and multiply it by 93million i get 1623156.204 million miles

Am I right?
• Oct 27th 2012, 08:55 PM
Soroban
Re: Word problem in Arcs
Hello, M670!

You're confusing yourself with a lot of extra work.

Quote:

Find the distance that the Earth travels in one day in its path around the Sun. Assume that a year
has 365 days and that the path of the Earth around the Sun is a circle of radius 93 million miles.

The circumference of a circle with radius $r$ is: . $C \:=\:2\pi r$

The circumference of the circular orbit of the Earth is: . $2\pi(93,\!000,\!000) \:=\:186,\!000,\!000\:\!\pi$ miles.

The Earth travels that distance in one year (365 days).

In one day, it travels: . $\frac{186,000,000\:\!\pi}{365} \:\approx\:1,\!600,\!921$ miles.

• Oct 30th 2012, 10:14 PM
Salahuddin559
Re: Word problem in Arcs
Yes, both are right.

Salahuddin
Maths online