How to solve for question 24. Find the surface area of the hemisphere given that the area of a great circle is 227.0 square kilometers.

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asked Jul 20, 2023 134k views

1 Answer

Zouying · Answer 1 · 2023-07-27T13:20:22+0000

Given that the are of the great circle is 227 km^2.

The hemisphere is the half of a sphere, the surfsce area wiill be:

SA= (1/2)surface area of the sphere+ base area

the curve surface area will be:

$(1)/(2)*4\pi r^2$

and we know that the base area is:

$\begin{gathered} BA=\pi r^2=227km^2 \\ r^2=(227km^2)/(\pi) \\ r=\sqrt[\placeholder{⬚}]{(227)/(\pi)}=8.5km \end{gathered}$

substituting:

$\begin{gathered} SA=(1)/(2)(4\pi r^2)+227km^2 \\ SA=2\pi(8.5km)^2+227km^2=680.96km^2 \end{gathered}$

The surface area is: 680.96 square kilometers.