A plane perpendicular to the Earth's axis and halfway between the poles cuts through the Earth's surface at the equator, which describes a circle on this plane. Every point on this circle is at the same distance from the north and south poles. If 48 inches are added to the Earth's equator, what change is made in the Earth's radius? Thank you.
+37084 Earth RADIUS = 3959 mi = 7918 mi DIAMETER = 501684480 inches
circumference = pi x diameter
pi x (501684480+48) - pi( 501684480) = 150.79 inches circumference increase
diameter increase is this divided by pi =47.979 inches radius increase=23.99 inches = ~~ 2 feet
Let 2.pi.r be the length of the Earth's equator. Then, if 48 inches is added to the equator, its length will be: 2pir + 48, and the Earth's radius r will be increased by x inches so that a new circle will be formed with radius: r + x. Using proportion between both circles, it then follows that:
r: (r+ x) =2pir: (2pir + 48), or: r/(r + x) =2pir/[2pir +48]. Therfore x =24/pi. Then x=24 / 3.141592 =~7.64 inches.
+129840 Let the original radius = R and let the change in radius = r
Then.....
The new circumference = 2* pi * R + 48 inches = 2 * pi * (R + r) .....so....
2* pi * R + 48 inches = 2 * pi (R + r) divide each side by 2 pi
R + 24 / pi inches = R + r subtract R from both sides
24 / pi inches = r ≈ 7.64 inches
