Surface area to volume ratioEdexcel A-Level Biology B: Subtopic test

1. 1
   A student made cubes of agar jelly containing a pH indicator, with sides of 2 mm, 4 mm and 8 mm, to model cells of different sizes. She placed them in dilute acid and timed how long the acid took to change the colour of the whole cube. (Surface area of a cube = 6 x side squared; volume = side cubed.)

   (a)

   What is the surface area to volume ratio of the 4 mm cube?

   [1 mark]

   • A3 : 1
   • B0.75 : 1
   • C1.5 : 1
   • D6 : 1

   (b)

   What happens to the surface area to volume ratio of the cubes as their side increases, and what is the consequence for diffusion?

   [1 mark]

   • AThe ratio increases, so diffusion supplies each unit of volume more quickly
   • BThe ratio decreases, so diffusion across the surface supplies each unit of volume more slowly
   • CThe ratio stays the same, so the rate is not affected by size
   • DThe ratio decreases, so diffusion distance to the centre becomes shorter

   (c)

   The 8 mm cube took much longer to change colour completely than the 2 mm cube. Explain this result.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The planarian is a flatworm about 15 mm long, 3 mm wide and less than 0.5 mm thick. It has no lungs, gills or blood. Its cells use oxygen from the water around it, which diffuses in across its body surface. A human, by contrast, is about 1.7 m tall and has lungs and a circulatory system.

   (a)

   Which statement explains how the planarian obtains oxygen without a circulatory system?

   [1 mark]

   • AOxygen is carried to its cells in the blood, as in a human
   • BIts small volume means it has no need for oxygen
   • COxygen enters by active transport across the body surface
   • DOxygen diffuses across its body surface to all its cells, because it has a large surface area to volume ratio and a short diffusion distance

   (b)

   Which is the best reason why a human needs a mass transport system?

   [1 mark]

   • AThe surface area to volume ratio is too small, and the diffusion distance too long, for diffusion alone to supply the inner cells
   • BHuman cells use no oxygen so need no direct supply
   • CMass transport increases the surface area to volume ratio of the whole body
   • DDiffusion cannot occur across cell surface membranes in humans

   (c)

   Explain how the shape of the planarian allows it to obtain enough oxygen without a circulatory system.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A spherical bacterium has a diameter of 2 µm, and a spherical human cell has a diameter of 20 µm. A human adult is a large multicellular organism made of many cells of this size. (Surface area of a sphere = 4πr²; volume of a sphere = 4/3 πr³.)

   (a)

   Calculate the surface area to volume ratio of each cell and state how many times greater it is for the bacterium than for the human cell.

   [3 marks]

   (b)

   Explain why a human needs a mass transport system and specialised gas exchange surfaces, but a bacterium does not.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student models organisms as cubes with sides of 1 mm, 10 mm and 100 mm. She assumes that the cells in each use oxygen at the same rate per unit volume, and that oxygen enters only by diffusion across the outer surface. She is also asked about a flatworm that is 100 mm long, 20 mm wide and 0.5 mm thick.

   (a)

   Using the cube model, explain why the 100 mm organism could not rely on diffusion across its surface alone, and describe what larger organisms need instead.

   [6 marks]

   (b)

   Evaluate the suggestion that a large organism could avoid the need for a mass transport system by being flat rather than cube-shaped.

   [6 marks]

   Total for question 4: 12 marks

End of questions