1 the Formula for Finding the Surface Area of a Sphere Is 4Πr2

Volume 27, Number 3, February 2015

Activity Size matters Bill Indge

1 The formula for finding the surface area of a sphere is 4πr2.

4 3 The formula for finding the volume of a sphere is 3 πr . (a) Explain how the surface area to volume ratio of a sphere may be calculated from the expression: surface area to volume ratio = 3/r. (3 marks) (b) Use this simplified expression to complete the table. (1 mark)

Surface area to volume Radius of sphere ratio

(c) Assume that a cell is spherical. Use the data in the table to describe the relationship between the size of a cell and its surface area to volume ratio. (1 mark) 2 The southern elephant seal is a very large mammal. Fully grown male elephant seals may reach a length of almost 5 m and have a mean body mass of 3200 kg. Elephant seals spend much of their lives in the cold waters around the sub-Antarctic islands. Explain the advantage of a large size to a mammal that lives in cold water. (3 marks) 3 Many species of earthworms burrow through the soil. Earthworms of one particular species may be up to 200 mm in length although their diameter is only 6 mm. (a) Explain the advantage to an earthworm of being covered in mucus. (2 marks) (b) The oxygen that earthworms require for respiration diffuses through their body surface into the blood vessels in the skin. Explain how the shape of a burrowing earthworm aids diffusion. (2 marks) (c) In dry conditions, soil-dwelling earthworms curl into a ball. Explain the advantage of this behaviour to an earthworm in dry conditions. (2 marks)

African elephants are the largest of all land mammals. Although geographically variable in size, fully mature males average over 3 m at the shoulder and have a mean body mass of around 5000 kg. Mature females are smaller and have corresponding measurements of 2.5 m and 3000 kg. Elephants formerly occurred throughout sub-Saharan Africa, wherever water and 5 trees were found. In spite of the animals’ size, elephants still manage to remain in thermal balance. Research in the 1970s led scientists to believe that spreading and flapping their highly vascularised ears plays an important role in regulating heat loss in these animals. The arteries in the ears are large in diameter and connected to veins by a dense capillary bed. Observations of wild 10 elephants showed that the frequency of ear flapping increased as the ambient temperature rose and decreased or ceased during cold weather. The rate of ear flapping was inversely related to wind velocity.

More recently, scientists have used infrared techniques to measure the heat radiated from the skin surface. This showed the presence of distinct thermal windows on the animal’s surface. 15 These thermal windows were particularly associated with the animal’s ears. Their frequency increased with the ambient temperature and body mass. It is now assumed that restriction of areas of increased blood flow to thermal windows might enable the elephant to react more flexibly to its needs regarding heat loss. Another habit of elephants is that of dust bathing. They use their trunks to gather dust and 20 blow it over their bodies. Observations of dust bathing in a herd of elephants showed that the frequency increased directly with temperature but was independent of body mass.

(a) The features of the blood vessels in the ears of an elephant described in the passage could result in heat loss (lines 8–9). Explain how. (3 marks) (b) If ear flapping plays an important role in heat loss, explain why you would expect its frequency to: (i) increase as the ambient temperature rose (lines 10–11) (2 marks) (ii) be inversely related to wind velocity (lines 11–12) (2 marks) (c) Explain what is meant by a ‘thermal window’ (line 14). (3 marks) (d) Explain how ‘restriction of areas of enhanced blood flow to thermal windows’ might enable an elephant to ‘react more flexibly to its needs regarding heat loss’ (lines 16–18). (2 marks) (e) The researchers investigating dust bathing concluded that its function was not related to thermoregulation. Identify and explain the evidence in the passage that supports this conclusion. (3 marks)

Philip Allan Updates © 2015 2 5 There are two systems by which sap moves through a plant. Xylem transports water and inorganic ions; phloem transports the products of photosynthesis. (a) Aphids feed on phloem sap. If a feeding aphid is anaesthetised and its body cut off, phloem sap continues to flow out through the mouthparts. Use your knowledge of the way in which phloem transports sap to explain why. (2 marks) (b) When a stem is cut under a solution of coloured dye, dye enters the xylem in the cut ends of the stem. Use your knowledge of the way in which sap travels through xylem to explain why. (3 marks) (c) Some insects feed on plant sap. These insects differ in size. Some, such as aphids are very small; others, such as the cicadas, are large. Scientists investigated body size in a large number of different species of sap-feeding insects. The graph shows their results.

(i) Describe the results shown in the graph. (2 marks) (ii) The mass of the muscles concerned with the mouthparts is directly proportional to body length in these insects. Use this information and your knowledge of the way in which sap is transported to suggest an explanation for the difference in body length of phloem feeders and xylem feeders. (4 marks)

Philip Allan Updates © 2015 3 Marking guidelines Note that these are only guidelines as to what might be expected in the answer. 1 (a) The surface area to volume ratio of a sphere is calculated by dividing its surface area by its volume. 4π r2

4 3 3 πr (1) Simplify by cancelling, in other words by dividing the top line and the bottom line by 4, π and r2. This gives: 1 1 3r (1) Multiply the top line and the bottom line by 3: 3 r (1) (3 marks) (b) The complete table should read:

Radius of Surface area to volume sphere ratio

(1 mark) (c) The larger a cell (as defined by its radius), the smaller the surface area to volume ratio; (1 mark) 2 Seals are mammals and have a high body temperature; Will lose less heat to the surrounding water; Because they have a small surface area to volume ratio; (3 marks) 3 (a) Acts as a lubricant; Enables the worm to move easily through the soil when burrowing; (2 marks) (b) The rate of diffusion is directly proportional to surface area;

Philip Allan Updates © 2015 4 Earthworm has large surface area to volume ratio; (2 marks) (c) Provides a smaller surface area to volume ratio; From which to lose water/for evaporation; (2 marks) 4 (a) Dense capillary bed provides large surface area; Large diameter of arteries ensures delivery of large volume of blood; Blood at core temperature/at higher temperature than that of the environment; (3 marks) (b) (i) Flapping will increase airflow over the ears/will increase heat loss by convection; Temperature gradient between body surface and surroundings lower/less heat can be lost to surroundings from body surface; (2 marks) (ii) As wind speed/velocity increases, more heat is lost; Ear flapping requires expenditure of energy by the elephant; (2 marks) (c) An area of increased blood flow; On skin/surface of animal; Associated with heat loss; (3 marks) (d) The use of thermal windows allows heat loss from small discrete areas; Which can be recruited independently; Allows finer control than from the whole body surface; (2 marks) (e) Frequency of dust bathing independent of body mass; Larger elephants have a smaller surface area to volume ratio; Larger elephants generate more metabolic heat; Expect frequency to increase with body mass; (3 marks) 5 (a) Sap in phloem is under pressure/at high pressure; Does not require aphid muscle contraction so continues to flow; (2 marks) (b) Sap in xylem is under tension; Tension released when stem is cut; Sap column contracts; Pulls dye into xylem; (3 marks) (c) (i) Most phloem feeders are small/xylem feeders are large in body length; Percentage of sap feeders feeding from phloem falls with increasing body length/sap feeders feeding from xylem increases with as body length increases; (2 marks) (ii) Sap under pressure in phloem; Therefore will flow along mouthparts/into gut of insect without muscle action; Muscles associated with feeding small allowing for small body size;

Philip Allan Updates © 2015 5 But sap under tension in xylem; or Sap under tension in xylem; Needs muscle action to overcome this tension; Muscles associated with feeding are large, suggesting large body size; But sap under pressure in phloem; (4 marks)

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