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: Identify the shape of C1.
C1 is a spherical epithelial cell with diameter
\[ 20\ \mu m \]

Step 2: Find the radius of C1.
\[ r=\frac{20}{2}=10\ \mu m \]

Step 3: Calculate surface area of spherical cell C1.
Surface area of a sphere is
\[ 4\pi r^2 \]
Therefore,
\[ S_1=4\pi(10)^2 \] \[ S_1=400\pi \]

Step 4: Identify the shape of C2.
C2 is a cube with side
\[ a=20\ \mu m \]

Step 5: Calculate surface area of cubic cell C2.
Surface area of a cube is
\[ 6a^2 \]
Thus,
\[ S_2=6(20)^2 \] \[ S_2=2400 \]

Step 6: Find the ratio of surface areas.
\[ \frac{S_1}{S_2} = \frac{400\pi}{2400} \] \[ = \frac{\pi}{6} \]

Step 7: Round off to two decimal places.
\[ \frac{\pi}{6}=0.5235\ldots \] \[ \boxed{0.52} \]