$$SA = 6 \times 2^2$ = 24$$ units$$^2$$, $$V = 2^3$ = 8$$ units$$^3$$, $$SA:V = 24/8 = 3$$

$$SA = 6 \times 1^2$ = 6$$ units$$^2$$, $$V = 1^3$ = 1$$ unit$$^3$$

$$SA = 4\pi \times 3^2$ = 36\pi$$, $$V = \frac{4}{3}\pi \times 3^3$ = 36\pi$$, $$SA:V = 36\pi / 36\pi = 1$$

$$SA = 1 \times 1 \times 6 \times 27 = 162$$ units$$^2$$

Question 1

Why do cells tend to be small in size?

Accepted Answer

Smaller cells have a higher surface area-to-volume ratio, optimizing the exchange of materials through the plasma membrane.

Question 2

Which formula correctly calculates the surface area of a spherical cell?

Accepted Answer

$$SA = 4\pi r^2$

Question 3

A cuboidal cell has a side length of 2 units. What is its surface area-to-volume ratio?

Accepted Answer

$$SA = 6 	imes 2^2$ = 24$$ units$$^2$$, $$V = 2^3$ = 8$$ units$$^3$$, $$SA:V = 24/8 = 3$$

Question 4

If a cell's radius doubles, how does its surface area-to-volume ratio change?

Accepted Answer

The surface area-to-volume ratio decreases.

Question 5

Which of the following is a consequence of a cell having a low surface area-to-volume ratio?

Accepted Answer

The cell loses efficiency in exchanging materials with its environment.

Question 6

Given a cuboidal cell with dimensions 1 unit x 1 unit x 1 unit, what is its surface area and volume?

Accepted Answer

$$SA = 6 	imes 1^2$ = 6$$ units$$^2$$, $$V = 1^3$ = 1$$ unit$$^3$$

Question 7

A spherical cell has a radius of 3 units. Calculate its surface area-to-volume ratio.

Accepted Answer

$$SA = 4\pi 	imes 3^2$ = 36\pi$$, $$V = \frac{4}{3}\pi 	imes 3^3$ = 36\pi$$, $$SA:V = 36\pi / 36\pi = 1$$

Question 8

Why is a high surface area-to-volume ratio important for cells?

Accepted Answer

It allows for efficient exchange of nutrients, waste, and thermal energy through the plasma membrane.

Question 9

Which of the following would most likely occur if a cell grows too large?

Accepted Answer

It becomes difficult to regulate what enters and leaves through the plasma membrane.

Question 10

A multicellular organism has cells of varying sizes. Which cells are likely to have the fastest rate of material exchange?

Accepted Answer

The smallest cells with the highest surface area-to-volume ratio.

Question 11

If a cuboidal cell is made up of 27 smaller cubes, each with a side length of 1 unit, what is the total surface area?

Accepted Answer

$$SA = 1 	imes 1 	imes 6 	imes 27 = 162$$ units$$^2$$

Question 12

Which of the following best explains why large cells lose efficiency in exchanging materials?

Accepted Answer

Their surface area does not increase as quickly as their volume, reducing the surface area-to-volume ratio.

Question 13

A spherical cell has a surface area of 314 units$$^2$$ and a volume of 523 units$$^3. $$What is its surface area-to-volume ratio?

Accepted Answer

$$SA:V = 314 / 523 = 0.6$$

Question 14

Which of the following is NOT a reason why cellular metabolism depends on cell size?

Accepted Answer

Larger cells have more DNA for metabolic reactions.

Question 15

If a cell's surface area is 54 units$$^2$$ and its volume is 27 units$$^3$$, what is its surface area-to-volume ratio?

Accepted Answer

$$SA:V = 54 / 27 = 2$$

Question 16

Which cell shape (cuboidal or spherical) generally has a higher surface area-to-volume ratio for the same volume?

Accepted Answer

Cuboidal cells

Question 17

A cell with a high surface area-to-volume ratio is most likely to:

Accepted Answer

Efficiently exchange materials with its environment.

Question 18

Which of the following is true about the relationship between cell size and heat exchange?

Accepted Answer

Smaller cells exchange heat more rapidly due to a higher surface area-to-volume ratio.

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

Study Guide - Practice Questions