Unit 2
6 marks · HardA scientist records the diameters of two distinct circular cells, Cell A and Cell B. The diameter of Cell A is 0.0036 mm and the diameter of Cell B is 2.8 × 10^{-2} mm.
Express the diameter of each cell in standard form.
The scientist wants to find out how many times bigger the area of Cell B is compared to the area of Cell A. Use the formula for the area of a circle, , and give your answer in standard form to 2 significant figures.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) Cell A: 3.6 × 10^{-3} mm; Cell B: 2.8 × 10^{-2} mm · must show Standard form correctly written with one digit before the decimal for each
(b) Area ratio ≈ 61 (6.1 × 10^1) · must show Use of correct area formula, Squaring each radius from standard form, Giving answer in standard form with 2 sig. fig.
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly converts at least one diameter to standard form.
A1 (a) · 1 mark · Both diameters correctly given in standard form (one digit before decimal, correct power of 10).
M2 (b) · 1 mark · Uses radius = diameter / 2 for each cell.
M3 (b) · 1 mark · Applies A = πr² for both cells (need not calculate π, may leave as a ratio of areas as fractions of π).
A2 (b) · 1 mark · Correctly calculates ratio of areas using laws of indices or calculator. (follow-through)
A3 (b) · 1 mark · Final answer given in standard form to 2 significant figures. (follow-through)
Worked solution
a) To express in standard form:
Cell A: 0.0036 mm = 3.6 × 10^{-3} mm
Cell B is already in standard form: 2.8 × 10^{-2} mm.
b) Radius of Cell A = 3.6 × 10^{-3} ÷ 2 = 1.8 × 10^{-3} mm
Radius of Cell B = 2.8 × 10^{-2} ÷ 2 = 1.4 × 10^{-2} mm
Area A = π (1.8 × 10^{-3})² = π × 3.24 × 10^{-6} = 3.24π × 10^{-6}
Area B = π (1.4 × 10^{-2})² = π × 1.96 × 10^{-4} = 1.96π × 10^{-4}
Ratio = Area B / Area A = (1.96π × 10^{-4}) / (3.24π × 10^{-6}) = (1.96 / 3.24) × 10^{2} ≈ 0.61 × 10^{2} = 6.1 × 10^{1} (to 2 sig. fig.)
So, area of Cell B is approximately 6.1 × 10^{1} times bigger than area of Cell A.