Numeracy Higher November 2018 Unit 1 Q13
13. Taryn made a birthday cake for her brother Carwyn, and placed it on a cake stand.
She made a cylindrical cake of radius 12 cm and height 10 cm.
To make the birthday cake look like the letter ‘C’ for Carwyn, she cut out a large slice.
The cake she has left has a uniform cross-section in the shape of a sector of a circle with sector angle 300°.
Diagram not drawn to scale
Taryn wants to put icing on all the visible surfaces of the cake.
Calculate the surface area that needs to be covered with icing.
Give your answer, in its simplest form, in terms of π. [5]
Surface area to be covered = …………… cm2
| Scheme | Marks | Comments |
|---|---|---|
| (Sector area =) \(\dfrac{300}{360} \times \pi \times 12^2\) (=120π) | B1 | Or equivalent Allow B1 for \(\dfrac{300}{360} \times \pi \times 12^2 \times 2\) |
| (Area of curved surface =) \(\dfrac{300}{360} \times 2 \times \pi \times 12 \times 10\) (=200π) | B1 | Or equivalent |
| \(\dfrac{300}{360}{\times}\pi{\times}12^2 + \dfrac{300}{360}{\times}2{\times}\pi{\times}12{\times}10 + 2{\times}12{\times}10\) | M2 | Or equivalent M1 for summing at least 3 terms with the equivalent of 2 of these terms correct May be seen in stages |
| = 320π + 240 (cm2) or 80(4π + 3) (cm2) or equivalent | A1 | CAO Mark final answer |