21M.1.SL.TZ1.2

pestleMathematicsAASLPaper 121M· sl-3-1-3d-space-volume-angles-distance-midpointssource ↗

The diameter of a spherical planet is $6 \times 10^{4} km$ .

Write down the radius of the planet.

[1]

The volume of the planet can be expressed in the form $π (a \times 10^{k}) {km}^{3}$ where $1 \leq a < 10$ and $k \in ℤ$ .

Find the value of $a$ and the value of $k$ .

[3]

Markscheme / solution

$3 \times 10^{4}$ OR $30000 (km)$ (accept $3 ∙ 10^{4}$ ) A1

[1 mark]

$\frac{4}{3} π {(3 \times 10^{4})}^{3}$ OR $\frac{4}{3} π {(30000)}^{3}$ (A1)

$= \frac{4}{3} π \times 27 \times 10^{12} (= π (36 \times 10^{12}))$ OR $= \frac{4}{3} π \times 27000000000000$ (A1)

$= π (36 \times 10^{13}) ({km}^{3})$ OR $a = 3.6, k = 13$ A1

[3 marks]

Examiners’ report

[N/A]