Calculate the volume of the balloon.

Calculate the radius of the balloon following this increase.

Units are required in parts (a) and (b).

\(\frac{4}{3}\pi  \times {6^3}\)    (M1)

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

\( = 905{\text{ c}}{{\text{m}}^3}{\text{ }}(288\pi {\text{ c}}{{\text{m}}^3},{\text{ }}904.778 \ldots {\text{ c}}{{\text{m}}^3})\)    (A1)     (C2)

Note:     Answers derived from the use of approximations of \(\pi \) (3.14; 22/7) are awarded (A0).

[2 marks]

Units are required in parts (a) and (b).

\(\frac{{140}}{{100}} \times 904.778 \ldots  = \frac{4}{3}\pi {r^3}\) OR \(\frac{{140}}{{100}} \times 288\pi  = \frac{4}{3}\pi {r^3}\) OR \(1266.69 \ldots  = \frac{4}{3}\pi {r^3}\)     (M1)(M1)

Note:     Award (M1) for multiplying their part (a) by 1.4 or equivalent, (M1) for equating to the volume of a sphere formula.

\({r^3} = \frac{{3 \times 1266.69 \ldots }}{{4\pi }}\) OR \(r = \sqrt[3]{{\frac{{3 \times 1266.69 \ldots }}{{4\pi }}}}\) OR \(r = \sqrt[3]{{(1.4) \times {6^3}}}\) OR \({r^3} = 302.4\)     (M1)

Note:     Award (M1) for isolating \(r\).

\((r = ){\text{ }}6.71{\text{ cm }}(6.71213 \ldots )\)     (A1)(ft)     (C4)

Note:     Follow through from part (a).

[4 marks]