Question: A marine biotechnologist is modeling the surface area of a circular culture dish with radius $ 3x $ meters and a cylindrical chamber of the same radius and height $ x $ meters built beneath it. What is the total surface area of the cylindrical chamber, excluding the bottom base?

Tue, 05 May 2026 22:21:23 +0000

**A marine biotechnologist is modeling the surface area of a circular culture dish with radius $ 3x $ meters and a cylindrical chamber of the same radius and height $ x $ meters built beneath it. What is the total surface area of the cylindrical chamber, excluding the bottom base?** In the evolving world of marine biotechnology, researchers are constantly refining how they design lab environments and cultivation systems. One common application involves integrating circular culture dishes with specialized cylindrical chambers used for controlled biological growth. A key architectural metric in these systems is surface area—critical for optimizing nutrient exchange, gas transfer, and light exposure. Now, a precise calculation centers on a cylindrical chamber beneath a circular culture dish: with a radius of $3x$ meters and height $x$ meters, what is the total surface area of that chamber—excluding the bottom base—used in this biotechnological setup? --- ### Why This Surface Area Matters in Modern Marine Research