- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
\begin{figure}[h]
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\caption{Figure 2}
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John picked 100 berries from a plant.
The largest berry picked was approximately 2.8 cm long.
The shape of this berry is modelled by rotating the curve with equation
$$16 x ^ { 2 } + 3 y ^ { 2 } - y \cos \left( \frac { 5 } { 2 } y \right) = 6 \quad x \geqslant 0$$
shown in Figure 2, about the \(y\)-axis through \(2 \pi\) radians, where the units are cm .
Given that the \(y\) intercepts of the curve are - 1.545 and 1.257 to four significant figures,
- use algebraic integration to determine, according to the model, the volume of this berry.
Given that the 100 berries John picked were then squeezed for juice,
- use your answer to part (a) to decide whether, in reality, there is likely to be enough juice to fill a \(200 \mathrm {~cm} ^ { 3 }\) cup, giving a reason for your answer.