Iron in the asteroid 16 Psyche is said to be valued at 8973 quadrillion euros EUR,where one quadrillion =1015.James believes the asteroid is approximately spherical with radius 113 km. He uses thisinformation to estimate its volume.

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$8.97\times {10}^{18}\left(\text{EUR}\right)\left(8.973\times {10}^{18}\right)$ (A1)(A1) (C2)

Note: Award (A1) for $8.97(8.973)$, (A1) for $\times {10}^{18}$. Award (A1)(A0) for $8.97\text{E}18$.
Award (A0)(A0) for answers of the type $8973\times {10}^{15}$.

[2 marks]

$\frac{4\times \mathrm{\pi }\times {113}^3}{3}$ (M1)

Note: Award (M1) for correct substitution in volume of sphere formula.

$6 040 000\left({\text{km}}^3\right)\left(6.04\times {10}^6,\frac{5771588\mathrm{\pi }}{3},6 043 992.82\right)$ (A1) (C2)

[2 marks]

$\left.\frac{6 043 992.82-6.074\times {10}^6}{6.074\times {10}^6}\right|\times 100$ (M1)

Note: Award (M1) for their correct substitution into the percentage error formula (accept a consistent absence of “$\times {10}^6$” from all terms).

$0.494\left(\%\right)\left(0.494026\dots \left(\%\right)\right)$ (A1)(ft) (C2)

Note: Follow through from their answer to part (b). If the final answer is negative, award at most (M1)(A0).

[2 marks]