Two cities have nearly the same north-south line of 110 degrees Upper W. The latitude of the first city is 23 degrees Upper F command the latitude of the second city is 36 degrees N. Approximate the distance between the cities if the average radius of Earth is 6400 km.

CORRECTED QUESTION:

Two cities have nearly the same north-south line of 110 degrees Upper W. The latitude of the first city is 23 degrees Upper N, and the latitude of the second city is 36 degrees N. Approximate the distance between the cities if the average radius of Earth is 6400 km.

ANSWER: 1452.11 km

Step-by-step explanation:

Since the two cities both lies on the Northern latitude of the sphere along  the same longitude, we are going to subtract the angles the latitude that each city subtend at the equator.

36 - 23 = 13 degrees   i.e the angles between the with two cities on a cross section the large circle formed by the longitude and its center.

Applying   the formula for the length of an arc on a sector on the large circle  

(∅/ 360) x 2πR

where, ∅ = is the angle between the two cities

R = radius of the Earth.

13/360 x 2 x π x 6400 = 1452.11 km

First find the radius by taking half the diameter. Use the radius to find the base area by using the formula for the area of a circle. Find the product of the base area and height, and then take one-third of the product.