A Standard globe representing the earth is 305 cm in diamete

A Standard globe representing the earth is 30.5 cm in diameter The equatorial circumference of the earth is about 24920 miles. The Circumference (Q of a sphere is C = D, (D - the diameter of the sphere.) Assume that the earth is a sphere. a) What is the scaie of the globe (lad? If you desire, you can use some unit of distance other than cm.) b) How many miles does one cm represent on the globe (x mi/cm)? [Calculate the circumference of the globe in cm and compare to the circumference of the earth in miles.]

Solution

(a) Given,

diameter of standard globe=30.5cm

circumference of earth=24920 miles

Now as we know,

1 mile=160934.4cm

therefore, 24920 miles=(24920*160934.4) cms

=4010485248 cms

now,finding the diameter of the earth,

3.14*D=4010485248 cms

D=4010485248/3.14 cms

=1277224601.27 cms

comparing both the diameters i.e.. diameter of globe and diameter of earth,so as to find the scale of the globe..

we get,

scale of globe=1277224601.27/30.5 cm

=41876216.44 cm

i.e.. 1 cm on globe represents 41876216.44 cm on the sphere(earth).

(b) 1 cm on globe = 41876216.44 cm on sphere

therefore, =41876216.44/160934.4 miles ( 1 cm = 1/160934.4 mi)

=260.21 miles