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A plane intersects the center of a sphere with the volume of about 9202.8 m. What is the area of the cross section?

User Michiyo
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1 Answer

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First, let's use the formula for the volume of a sphere to find its radius:


\begin{gathered} V=(4)/(3)\pi r^3\\ \\ 9202.8=(4)/(3)\cdot3.1416\cdot r^3\\ \\ r^3=(9202.8)/((4)/(3)\cdot3.1416)\\ \\ r^3=2197\\ \\ r=13\text{ m} \end{gathered}

Now, to calculate the area, let's use the formula for the area of a circle:


\begin{gathered} A=\pi r^2\\ \\ A=3.1416\cdot13^2\\ \\ A=530.9\text{ m^^b2} \end{gathered}

User Cinek
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