A.4 Geometry and trigonometry

Learning objectives

—A.4.1—Circumference, area and volumeCalculate circumferences, surface areas and volumes of regular shapes, including circles, rectangular and cylindrical prisms and spheres, and apply these calculations to cells.

Identify the idealised shape and whether the question asks for a boundary length, surface area or enclosed volume. Convert every dimension to one unit before applying powers, and report linear, squared or cubed units to match the quantity.

Shape	Boundary/surface area	Volume
Circle	Circumference $C=2\pi r$ ; area $A=\pi r^2$	—
Rectangular prism	$SA=2(lw+lh+wh)$	$V=lwh$
Cylindrical prism	Total $SA=2\pi r^2+2\pi rh$ ; curved area $=2\pi rh$	$V=\pi r^2h$
Sphere	$SA=4\pi r^2$	$V=\frac{4}{3}\pi r^3$

A chloroplast image has diameter 96 mm at $\times16{,}000$ . Convert $96$ mm to $96{,}000$ µm, then actual diameter $=96{,}000/16{,}000=6.0$ µm and radius $=3.0$ µm. Approximating it as a sphere, $SA=4\pi(3.0)^2=113$ µm $^2$ to a whole number.

Surface-area-to-volume ratio requires separate calculations followed by division. For similar shapes, area scales with length squared and volume with length cubed, so enlarging a cell lowers its SA:V even when its shape is unchanged.

Radius is half the diameter. Do not use curved cylinder area when total surface area is required, mix units before squaring/cubing, or report surface area in volume units.

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—Pearson Edexcel IAL BiologyRead