Question

1.3.1 test (cst): cell biology unit test
question 5 of 10
epithelial cells that line the villi of the small intestine absorb nutrients into the blood and release wastes out of the blood for removal from the body. ideally, an epithelial cell has a large surface area for greater absorption of nutrients, but it is also important for epithelial cells to have a low volume, so nutrients can quickly pass to other cells. predict which of the following cells has the most efficient nutrient absorption and waste elimination.
cell a
cell b
a. cell b, because its volume is greater than its surface area.
b. cell b, because it has the larger surface - area - to - volume ratio.
c. cell a, because its volume is greater than its surface area.
d. cell a, because it has the larger surface - area - to - volume ratio.

Explanation:

Step1: Calculate surface area of a cube

The surface area formula for a cube is \(SA = 6s^{2}\). For Cell A (\(s = 10\mu m\)), \(SA_A=6\times(10)^{2}=600\mu m^{2}\). For Cell B (\(s = 50\mu m\)), \(SA_B = 6\times(50)^{2}=15000\mu m^{2}\).

Step2: Calculate volume of a cube

The volume formula for a cube is \(V=s^{3}\). For Cell A (\(s = 10\mu m\)), \(V_A=(10)^{3}=1000\mu m^{3}\). For Cell B (\(s = 50\mu m\)), \(V_B=(50)^{3}=125000\mu m^{3}\).

Step3: Calculate surface - area - to - volume ratio

The ratio formula is \(\text{Ratio}=\frac{SA}{V}\). For Cell A: \(\text{Ratio}_A=\frac{600}{1000}=0.6\). For Cell B: \(\text{Ratio}_B=\frac{15000}{125000}=0.12\). Since \(0.6>0.12\), Cell A has a larger surface - area - to - volume ratio. A higher surface - area - to - volume ratio means more efficient nutrient absorption (due to more surface area for absorption) and waste elimination (as substances have to travel less distance within the cell, which is related to the volume).

Answer:

D. Cell A, because it has the larger surface - area - to - volume ratio.