Question 1

Why do cells need a high surface area-to-volume (SA:V) ratio?

Accepted Answer

To maximize the rate of exchange of materials through the plasma membrane

Question 2

A spherical cell has a radius $$r. $$Which formula correctly gives its surface area?

Accepted Answer

$$SA = 4\pi r^2$

Question 3

If a cell increases its radius from $$r to$$ $$2r$$, how does its surface area-to-volume ratio change?

Accepted Answer

It decreases by half

Question 4

Which of the following best explains why large cells are less efficient at exchanging materials with their environment?

Accepted Answer

Their surface area-to-volume ratio is lower, reducing the rate of exchange per unit volume

Question 5

Given a cuboidal cell with side length $$S$$, what is the formula for its surface area-to-volume ratio?

Accepted Answer

$$\frac{6S^2$}{S^3$}$$

Question 6

A scientist compares a single large cube-shaped cell (side = 30 $$\mum) to 27 $$smaller cube-shaped cells (side = 10 $$\mum $$each). Which has the greater total surface area and why?

Accepted Answer

The 27 small cells, because the total surface area increases as cell size decreases

Question 7

Which of the following is a real-world consequence of a low surface area-to-volume ratio in large cells?

Accepted Answer

Reduced efficiency in removing cellular waste

Question 8

If a spherical cell has a surface area of $$314$$ units$$^2$$ and a volume of $$523.3$$ units$$^3$$, what is its surface area-to-volume ratio?

Accepted Answer

$$0.6$$

Question 9

Why do red blood cells have a biconcave shape?

Accepted Answer

To increase their surface area-to-volume ratio for efficient gas exchange

Question 10

Which of the following best describes the relationship between cell size and metabolic demand?

Accepted Answer

As cell size increases, metabolic demand increases faster than the ability to exchange materials

Question 11

A cell is modeled as a sphere. If its radius triples, by what factor does its volume increase?

Accepted Answer

27

Question 12

Which of the following is NOT a reason why cells tend to be small?

Accepted Answer

Small cells have a lower surface area-to-volume ratio

Question 13

Which formula correctly gives the volume of a sphere with radius $$r$$?

Accepted Answer

$$V = \frac{4}{3}\pi r^3$

Question 14

A cell's ability to dissipate thermal energy is most directly related to which property?

Accepted Answer

Its surface area

Question 15

Which of the following would most likely be true for a cell with a very low surface area-to-volume ratio?

Accepted Answer

It would struggle to obtain enough nutrients to support its metabolism

Question 16

If a cell is shaped as a cube with side length $$S = 2$$ units, what is its surface area-to-volume ratio?

Accepted Answer

$$1.5$$

Question 17

Which adaptation would you expect to find in cells specialized for absorption, such as intestinal epithelial cells?

Accepted Answer

Microvilli to increase surface area

Question 18

A frog egg is much larger than a typical animal cell. Which of the following is a likely adaptation that allows it to survive despite its low surface area-to-volume ratio?

Accepted Answer

It contains large stores of nutrients to support early development

Question 19

Which of the following best explains why multicellular organisms can grow larger than unicellular organisms?

Accepted Answer

They are composed of many small cells, each with a high surface area-to-volume ratio

Cell Size and Surface Area-to-Volume Ratio in Biology

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