Higher June 2023 Paper 3 Q18
18 A solid frustum is made by removing a small cone from a large cone as shown in the diagram.
The slant height of the small cone is 6 cm.
The slant height of the large cone is 10 cm.
The radius of the base of the large cone is 3 cm.
Calculate the total surface area of the frustum.
Give your answer correct to 3 significant figures. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 98.8 | P1 | for process to find the radius of the top of the frustum eg \(6 \div 10 \times 3\ (= 1.8)\) |
| P1 | for process to find the curved surface area of the frustum eg \(3 \times \pi \times 10 - \text{``}1.8\text{''} \times \pi \times 6\ (= 60.3\ldots)\) | |
| P1 | for process to find the area of either circular face eg \(\pi \times 3^2\ (= 28.27\ldots)\) or \(\pi \times {\text{``}1.8\text{''}}^2\ (= 10.1\ldots)\) | |
| P1 | for a process to find the curved surface area + the area of at least one circular face eg \(3 \times \pi \times 10 - \text{``}1.8\text{''} \times \pi \times 6 + \pi \times 3^2\ (= 88.5\ldots)\) or \(3 \times \pi \times 10 - \text{``}1.8\text{''} \times \pi \times 6 + \pi \times {\text{``}1.8\text{''}}^2\ (= 70.49\ldots)\) | |
| A1 | for an answer in the range 98.7 to 98.8 |
Additional guidance
Accept rounded or truncated values
Accept multiples of \(\pi\) for process marks.
If a correct answer within the range is shown in working but incorrectly rounded award full marks.