Question

Consider a spherical epithelial cell (C1) of diameter \(20\ \mu m\) and a cubic shaped liver cell (C2) of side \(20\ \mu m\). The ratio of the surface areas of C1 : C2 is _ _ _. (round off to two decimal places)

Hint:

For a sphere, surface area is \(4\pi r^2\), while for a cube, surface area is \(6a^2\). Always convert diameter to radius before using the sphere formula.

Answer 1

Correct Answer: 0.52

Step 1: Set up the sphere.
Cell C1 is a sphere of diameter $20\ \mu m$, so its radius is $10\ \mu m$. Its surface area is \[ 4\pi r^2 = 4\pi(10)^2 = 400\pi \]

Step 2: Set up the cube.
Cell C2 is a cube of side $20\ \mu m$. Its surface area is \[ 6a^2 = 6(20)^2 = 2400 \]

Step 3: Form the ratio.
\[ \frac{S_1}{S_2} = \frac{400\pi}{2400} = \frac{\pi}{6} \]

Step 4: Evaluate.
\[ \frac{\pi}{6} = 0.5235\ldots \approx 0.52 \]

Step 5: Answer.
\[ \boxed{0.52} \]