Surface area to volume ratioAQA A-Level Biology: Subtopic test

1. 1
   Biology students make cube-shaped models of organisms to investigate how size affects the exchange of substances. They compare a small cube with sides of 3 cm and a larger cube with sides of 6 cm.

   (a)

   What is the surface area to volume ratio of the cube with sides of 3 cm?

   [1 mark]

   • A0.5 : 1
   • B1.5 : 1
   • C2 : 1
   • D6 : 1

   (b)

   How does the surface area to volume ratio of the 6 cm cube compare with that of the 3 cm cube?

   [1 mark]

   • AIt is half as large
   • BIt is twice as large
   • CIt is the same
   • DIt is one quarter as large

   (c)

   Explain why an organism the size of the 6 cm cube is less able to exchange substances by diffusion across its body surface alone than one the size of the 3 cm cube.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A shrew has a body mass of about 8 g and must feed almost continuously. An elephant has a body mass of about 4000 kg and eats for much of the day, but eats far less food for each kilogram of its body mass. Both are mammals that maintain a constant body temperature.

   (a)

   Which statement best explains why the shrew has a higher metabolic rate per gram of body mass than the elephant?

   [1 mark]

   • AThe shrew has a smaller surface area to volume ratio, so it retains more heat
   • BThe shrew has a larger volume, so it produces more heat for each gram
   • CThe shrew is warm-blooded and the elephant is not
   • DThe shrew has a larger surface area to volume ratio, so it loses heat faster and must respire faster to replace it

   (b)

   Which feature would reduce heat loss for a small mammal living in a cold climate?

   [1 mark]

   • ALong, thin legs
   • BA short, rounded body with small ears
   • CLarge, thin ears with many blood vessels
   • DA flattened body shape

   (c)

   Elephants have very large, thin ears with many blood vessels near the surface. Explain how this helps an elephant to lose heat despite its small surface area to volume ratio.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two cube-shaped model organisms are made. Organism A has sides of 1 cm and organism B has sides of 4 cm. The cells in both models respire at the same rate for each cm³ of volume.

   (a)

   Calculate the surface area to volume ratio of organism A and of organism B. Show your working.

   [3 marks]

   (b)

   Explain why organism B could not obtain enough oxygen by diffusion across its body surface alone, and describe two ways in which real large organisms overcome this problem.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Biologists investigate how body size and shape affect heat loss in mammals. They compare a fennec fox, which lives in hot deserts and has ears about 15 cm long, with an Arctic fox, which lives in cold tundra and has a compact, rounded body and ears about 6 cm long. They also model a mouse and an elephant as cubes with sides of 2 cm and 200 cm.

   (a)

   Explain how the body shapes of the fennec fox and the Arctic fox are adaptations to their different climates.

   [6 marks]

   (b)

   Calculate the surface area to volume ratio of the mouse cube and of the elephant cube. Use your results to explain why the mouse has a much higher metabolic rate per gram of body mass than the elephant.

   [6 marks]

   Total for question 4: 12 marks

End of questions