Sphere cuts

At what distance from the centre does a plane intersect a sphere of radius R = 46, if the area of the circular cross-section and the area of the great circle are in the ratio 2:5?

Final Answer:

x =  35.6

Step-by-step explanation:

$$\begin{gathered} R=46 \\ {S}_1:S_2=2:5 \\ \pi r^2:\pi R^2=2:5 \\ {r}^2:R^2=2:5 \\ x=R\cdot \sqrt{1-\frac{2}{5}}=46\cdot \sqrt{1-\frac{2}{5}}=35.6 \end{gathered}$$

Try another example