Higher November 2024 Paper 1 Q22
22 The diagram shows a bowl in the shape of a hemisphere.
The bowl is made from metal.
Diagram NOT accurately drawn
The outer radius of the bowl is 12 cm
The inner radius of the bowl is 9 cm
The thickness of the bowl is uniform.
Work out the volume of the metal.
Give your answer correct to the nearest whole number.
(3)
| Scheme | Marks |
|---|---|
\(\dfrac{1}{2} \times \dfrac{4}{3} \times \pi \times 12^3\;(= 1152\pi = 3619.(114))\) oe or \(\dfrac{1}{2} \times \dfrac{4}{3} \times \pi \times 9^3\;(= 486\pi = 1526.(814))\) oe or \(\dfrac{4}{3} \times \pi \times 12^3\;(= 2304\pi = 7238(.229))\) oe or \(\dfrac{4}{3} \times \pi \times 9^3\;(= 972\pi = 3053(.628))\) oe | M1 |
\(\dfrac{1}{2} \times \dfrac{4}{3} \times \pi \times 12^3 - \dfrac{1}{2} \times \dfrac{4}{3} \times \pi \times 9^3\) oe or \(\text{``}{1152\pi}\text{''} - \text{``}{486\pi}\text{''}\;(= 666\pi)\) oe or \(\dfrac{\frac{4}{3} \times \pi \times 12^3 - \frac{4}{3} \times \pi \times 9^3}{2}\) oe or \(\dfrac{\text{``}{2304\pi}\text{''} - \text{``}{972\pi}\text{''}}{2}\left(= \dfrac{1332\pi}{2} = 666\pi\right)\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 2092 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for finding the volume of a sphere or a hemisphere
A1: 2091 – awrt 2093