A fruit display bowl in a corner shop is a hemisphere of radius 15 cm, as shown. The shopkeeper wants the figure before choosing where the bowl will sit on ...
Question 1 Report
A fruit display bowl in a corner shop is a hemisphere of radius 15 cm, as shown. The shopkeeper wants the figure before choosing where the bowl will sit on the counter. Apples and oranges are refreshed on top of the display each morning.
Work out the volume of the bowl. Give your answer correct to 3 significant figures. (3)
Answer Details
The fruit bowl is a hemisphere, exactly half of a sphere. Its volume is half of the full sphere formula: \( V = \dfrac{2}{3}\pi r^3 \).
\[ V = \frac{2}{3}\pi (15)^3 = \frac{2}{3}\pi \times 3375 = 2250\pi = 7068.58\ldots \text{ cm}^3 \]Rounded to 3 significant figures, the volume of the bowl is \(7070\) cm\(^3\). [3] (1 for \(\frac{2}{3}\pi (15)^3\), 1 for the unrounded value, 1 for 7070 to 3 s.f.)
A hemisphere's volume formula is exactly half of the full sphere's \( \frac{4}{3}\pi r^3 \); using the full sphere formula by mistake would double the correct answer.
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