Table 22.1 gives measurements from drawings of three protoctists, including the Amoeba shown in Fig. 22.1. Some values are missing. Fig. 22.1 Table 22.1 Spe...

All parts use one relationship: magnification \(=\dfrac{\text{image size}}{\text{actual size}}\), rearranged as needed. Keep the units consistent.

(a) Value X [2]: \(X=\dfrac{\text{image}}{\text{actual}}=\dfrac{90}{0.45}=\times 200\) [2] (both widths in mm, so X is just a number).

(b) Value Y [2]: rearranging, image \(=\) actual \(\times\) magnification, so \(Y=0.30\times 150=45\text{ mm}\) [2].

(c) Value Z [2]: rearranging, actual \(=\dfrac{\text{image}}{\text{magnification}}\), so \(Z=\dfrac{84}{200}=0.42\text{ mm}\) [2].

(d) Convert Z to micrometres [1]: \(1\text{ mm}=1000\,\mu m\), so \(0.42\times 1000=420\,\mu m\) [1].

(e) Why the real sizes differ so much from the drawings [3]: the drawings are magnified / enlarged [1]; each one by the magnification shown [1]; so the drawing is many times bigger than the real organism [1]. A magnification of ×200, for example, means every length on the drawing is 200 times the true length.

(f) Why Amoeba's width is hard to measure exactly [3]: Amoeba has no fixed shape / it keeps changing shape [1]; the pseudopodia extend and retract as it moves and feeds [1]; so the value taken for its "width" depends on the moment at which it is measured [1]. This is why organisms with a definite outline, such as Paramecium, give repeatable measurements while Amoeba does not.