Solved: Iron in the asteroid 16 Psyche is said to be valued at 8973 quadrillion euros... [IB Mathematics Applications & Interpretation (AI)]

Solved: Iron in the asteroid 16 Psyche is said to be valued at 8973 quadrillion euros... [IB Mathematics Applications & Interpretation (AI)] | RevisionDojo

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Question

SLPaper 1

Iron in the asteroid 16 Psyche is said to be valued at $8973$ quadrillion euros $(EUR)$ ,where one quadrillion $= 10^{15}$ .

James believes the asteroid is approximately spherical with radius $113 km$ . He uses thisinformation to estimate its volume.

Write down the value of the iron in the form $a \times 10^{k}$ where $1 \leq a < 10, k \in ℤ$ .

[2]

Verified

Solution

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

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

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

[2 marks]

Calculate James’s estimate of its volume, in ${km}^{3}$ .

[2]

Verified

Solution

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

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

$6 040 000 ({km}^{3}) (6.04 \times 10^{6}, \frac{5771588 π}{3}, 6 043 992.82)$ (A1) (C2)

[2 marks]

The actual volume of the asteroid is found to be $6.074 \times 10^{6} {km}^{3}$ .

Find the percentage error in James’s estimate of the volume.

[2]

Verified

Solution

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

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

$0.494 (%) (0.494026 \dots (%))$ (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]

Mathematics Applications & Interpretation (AI) International Baccalaureate (IB) Practice Question: Iron in the asteroid 16 Psyche is said to be valued at 8973 quadrillion euros EUR,where one quadrillion =1015.James beli...