If you want to know the area of a circle to 1.00 percent accuracy, determine how
ID: 1417049 • Letter: I
Question
If you want to know the area of a circle to 1.00 percent accuracy, determine how accurately you should measure the radius of the circle expressed in percent? (b) Suppose that the circumference of Earth is a perfect circle of exactly 40, 000, 000 m. Somebody prepares a wire that is supposed to go around the equator completely, but makes it 1.000 m too long by mistake. If this 1.000 m too long wire were placed around the earth in a perfect circle centered upon the center of the earth, what would be the distance of the wire off the ground?Explanation / Answer
A=r2
dA=2rdr=2(r2)(dr/r)=2A(dr/r)
so
(dA/A)=2(dr/r)
(dA/A) * 100=2(dr/r) * 100
(dr/r) * 100=1/2 *(dA/A) * 100
(dr/r) * 100= 1/2 * 1
(dr/r) * 100= 0.5 percent
Part b) Circumference C=40,000,000 m
R=C/2
R=40,000,000/2 * 3.14
R=6.369426.7516 m
Now the circumeference becomes Cnew =40,000,001 m( it increases by 1 metre)
Rnew= 40,000,001/2* 3.14=6369426.9108
Difference in R= Rnew- R=6369426.9108 -6.369426.7516 m
Difference in R=distance of wire of the ground =0.1592 metres
GOOD LUCK!!!