Question

compare the surface-area-to-volume ratios of the three spheres representing cells.
radius: 1
surface area: 4π
volume: \\(\frac{4}{3}π\\)
radius: 2
surface area: 16π
volume: \\(\frac{32}{3}π\\)
radius: 3
surface area: 36π
volume: \\(\frac{108}{3}π\\)
which of the three cells, if any, has the greatest surface-area-to-volume ratio?
a. the cell with radius 1
b. the cell with radius 2
c. the cell with radius 3
d. all three cells have the same surface-area-to-volume ratio.

Explanation:

Step1: Calculate ratio for radius 1

$\text{Ratio} = \frac{4\pi}{\frac{4}{3}\pi} = 3$

Step2: Calculate ratio for radius 2

$\text{Ratio} = \frac{16\pi}{\frac{32}{3}\pi} = \frac{16 \times 3}{32} = 1.5$

Step3: Calculate ratio for radius 3

$\text{Ratio} = \frac{36\pi}{\frac{108}{3}\pi} = \frac{36 \times 3}{108} = 1$

Step4: Compare the three ratios

$3 > 1.5 > 1$

Answer:

A. The cell with radius 1