Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 12.2
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Exercise 71 Page 673

The surface area of a sphere is 4 π r^2, where r is the radius of the sphere.

The surface of the Earth's moon is smaller than the area of Asia, but greater than the area of Africa.

Practice makes perfect

We want to compare the surface area of the Moon with the areas of the Earth's continents. These areas are listed in the decreasing order in the following table.

Continent Area (square miles)
Asia 17 212 048. 1
Africa 11 608 161. 4
North America 9 365 294. 0
South America 6 879 954. 4
Antarctica 5 100 023. 4
Europe 3 837 083. 3
Australia/Oceania 2 967 967. 3
Earth's moon has a roughly spherical shape, so let's recall the formula for the surface area S of a sphere. S = 4 π r^2 Here, r is a radius of the sphere. The radius of the Earth's moon is 1080 miles. We can substitute this value for r into the above formula to find the approximate surface area of the Moon. Let's do it!
S = 4 π r^2
S = 4 π ( 1080)^2
S = 4 π (1 166 400)
S = 4 665 600π
S = 14 657 414.6846...
S ≈ 14 657 414.7
The surface area of the Moon is about 14 657 414.7 square miles. Now, let's add the row for the Moon to our table, making sure to keep the table in the descending order.
Continent Area (square miles)
Asia 17 212 048. 1
Moon 14 657 414.7
Africa 11 608 161. 4
North America 9 365 294. 0
South America 6 879 954. 4
Antarctica 5 100 023. 4
Europe 3 837 083. 3
Australia/Oceania 2 967 967. 3

As we can see, the surface of the Earth's moon is smaller than the area of Asia, but greater than the area of Africa.