Assume that the Earth is a sphere with a radius, \(r\) , of \(6.38 \times {10^3}\,{\text{km}}\) .

i)     Calculate the surface area of the Earth in \({\text{k}}{{\text{m}}^2}\).

ii)    Write down your answer to part (a)(i) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\) .

The surface area of the Earth that is covered by water is approximately \(3.61 \times {10^8}{\text{k}}{{\text{m}}^2}\) .

Calculate the percentage of the surface area of the Earth that is covered by water.

i)     \(4\pi {(6.38 \times {10^3})^2}\)       (M1)

Note: Award (M1) for correct substitution into the surface area of a sphere formula.

\( = 512\,000\,000\,\,\,(511506576,\,\,162\,817\,600\pi )\)       (A1)    (C2)

Note: Award at most (M1)(A0) for use of \(3.14\) for \(\pi \), which will give an answer of \(511\,247\,264\).

ii)    \(5.12 \times {10^8}\,\,\,(5.11506... \times {10^8},\,\,1.628176\pi  \times {10^8})\)       (A1)(ft)(A1)(ft)    (C2)

Note: Award (A1) for \(5.12\) and (A1) for \( \times {10^8}\).
Award (A0)(A0) for answers of the type: \(5.12 \times {10^7}\).
Follow through from part (a)(i).

\(\frac{{3.61 \times {{10}^8}}}{{5.11506...\,\, \times {{10}^8}}} \times 100\)  OR \(\frac{{3.61}}{{5.11506...\,}} \times 100\)  OR \(0.705758... \times 100\)        (M1)

Note: Award (M1) for correct substitution. Multiplication by \(100\) must be seen.

\( = 70.6\,(\% )\,\,\,\,(70.5758...\,(\% ))\)        (A1)(ft)   (C2)

Note: Follow through from part (a). Accept the use of \(3\) sf answers, which gives a final answer of \(70.5\,(\% )\,\,\,\,(70.5758...\,(\% ))\) .

Question 1: Surface area of a sphere; scientific notation and percentage.
The weakest candidates were unable to square a number given in scientific notation or write the answer in scientific notation. Weaker candidates used the area of a circle formula rather than the surface area of a sphere. Premature rounding caused some candidates to obtain an incorrect final answer. Many candidates confused percentage of a quantity with percentage error or found the reciprocal of the correct answer. Overall this question was well attempted.

Question 1: Surface area of a sphere; scientific notation and percentage.
The weakest candidates were unable to square a number given in scientific notation or write the answer in scientific notation. Weaker candidates used the area of a circle formula rather than the surface area of a sphere. Premature rounding caused some candidates to obtain an incorrect final answer. Many candidates confused percentage of a quantity with percentage error or found the reciprocal of the correct answer. Overall this question was well attempted.