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The area outside the square but inside the circle is:
25\pi - 50 = 25(\pi - 2) \text{ μm}^2
Thus, the region's area is $ \boxed{25(\pi - 2)} $.
Question: A sustainable energy facility uses a cylindrical battery casing with radius $ 2x $ and height $ 5x $. A spherical capacitor of radius $ 3x $ is placed inside. What is the ratio of the volume of the spherical capacitor to the volume of the cylindrical casing?
Solution: Volume of the sphere:
\frac{4}{3}\pi (3x)^3 = \frac{4}{3}\pi (27x^3) = 36\pi x^3
Volume of the cylinder:
\pi (2x)^2 (5x) = \pi (4x^2)(5x) = 20\pi x^3
\frac{36\pi x^3}{20\pi x^3} = \frac{36}{20} = \frac{9}{5}
Thus, the ratio is $ \boxed{\dfrac{9}{5}} $.Question: A museum curator is cataloging a collection of 48 ancient tablets. If the ratio of inscribed tablets to plain tablets is $5:3$, and all inscribed tablets must be displayed in groups of 7, what is the greatest number of inscribed tablets that can be grouped without leaving any out?