The meter was originally defined as one 10 millionth of the distance from the equator to the north pole. Using

Question

The meter was originally defined as one 10 millionth of the distance from the equator to the north pole. Using this information.(Using a calculator)

a) What is the circumference of the earth in kilometers?

b) What is the radius of the earth?

c) What is the surface area of the earth in km^2? Express your answer in scientific notation.

d) What is the volume of the earth in km^3?

Answer 1

the earth is roughly a ball or sphere

for comparison:To my knowledge, the meter was defined originally by a 1/40000 km of the earth's circumference

Equator to north-pole=1/4 circumference (1/4 circle)

PI=3.1415926

circumference C  =same as circle

C = 2 r PI = D PI                       with  diameter D =2r, radius r

Volume V=1/6 D^3 PI  

Volume V=4/3 r^3 PI

Surface area S=4 r^2 PI

Answer 2

let d = distance from equator to the north pole

1 m = (10^-7)d

d= 1/(10^-7)

d = 10^7 m

a) circumference is 4 times d

C = 4 x 10^7 m

C = 4 x 10^4 km

b) C = 2(pi)r

r = C/2(pi)

r = (4 x 10^4 )/(2 x 3.14)

r =6.4 x 10^3 km

c) A = 4(pi)r^2

A = 4(3.14)(6.4x10^3 km)^2

A = 5.1 x 10^8 km^2

d) V =4/3 (pi) r^3

V = 4/3(3.14)(6.4x10^3)^3

V = 1.1 x 10^12 km^3