Higher November 2023 Paper 3 Q19
19
The diagram above shows a frustum F of a cone.
The frustum is made by removing a cone with height 10 cm from a solid cone with height 15 cm and base diameter 24 cm.
The solid S is made by removing F from a solid hemisphere as shown in the diagram below.
The hemisphere has diameter 24 cm.
Calculate the volume of solid S.
Give your answer correct to 3 significant figures. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 2030 | P1 | for process to find diameter of base of small cone, eg 16 seen as diameter or 8 seen as radius or for scale factor (length) is \(\tfrac{2}{3}\) oe or \(\tfrac{3}{2}\) oe |
| P1 | for process to find the volume of one cone, eg \(\tfrac{1}{3} \times \pi \times 12^2 \times 15\ (= 720\pi\) or \(2261.946\ldots)\) or \(\tfrac{1}{3} \times \pi \times \text{``}8\text{''}^2 \times 10\ \left(= \tfrac{640}{3}\pi\right.\) or \(\left.670.206\ldots\right)\) or for process to find the volume of the hemisphere, eg \(\tfrac{2}{3} \times \pi \times 12^3\ (= 1152\pi\) or \(3619.114\ldots)\) or for scale factor (volume) is \(\left(\tfrac{2}{3}\right)^3\) oe | |
| P1 | for full process to find volume of frustum and hemisphere, eg \(\text{``}2261.946\ldots\text{''} - \text{``}670.206\ldots\text{''}\ \left(= \tfrac{1520}{3}\pi\right.\) or \(\left.1591.740\ldots\right)\) or \(\text{``}2261.946\ldots\text{''} \times \left(1 - \left(\tfrac{2}{3}\right)^3\right)\) and \(\left(\tfrac{4}{3} \times \pi \times 12^3\right) \div 2\) oe \((= 1152\pi\) or \(3619.114\ldots)\) | |
| A1 | for answer in the range 2026 to 2030 |
Additional guidance
If an answer is shown in the range in working and then incorrectly rounded award full marks.