7. Surface Areas and Volumes of Spheres
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Remember that the Western Hemisphere is not a true hemisphere, it is just half of the surface area of the Earth.
Approximately 98 677 751.7 square miles
To find the surface area of the Western Hemisphere, we need to find the surface area of Earth and divide it by 2. Let's remember the area for the surface area of a sphere. \begin{gathered} SA_\text{sphere}=4\pi r^2 \end{gathered} We will not use the formula for the surface area of a hemisphere because this is not a true hemisphere, it is just half of the surface of the Earth. Now we need the radius of Earth. We are given that the circumference C of Earth is about 24 900 miles. Let's recall the formula for circumference. C=2Ï€ r We can substitute 24 900 for C and solve for the radius r.
C= 24 900
.LHS /2Ï€.=.RHS /2Ï€.
Rearrange equation
Round to 2 decimal place(s)
We can substitute this value into the formula for the surface area of a sphere and simplify.
r= 3962.96
Calculate power and product
Finally, we can divide this number by 2 to get the surface area of the Western Hemisphere only. \begin{gathered} SA_\text{WH}=\dfrac{197\,355\,503.467}{2}=98\,677\,751.7336 \end{gathered} The surface area of the Western Hemisphere is approximately 98 677 751.7 square miles.