| Date | May Specimen | Marks available | 2 | Reference code | SPM.1.sl.TZ0.12 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Calculate | Question number | 12 | Adapted from | N/A |
Question
A child’s toy consists of a hemisphere with a right circular cone on top. The height of the cone is \(12{\text{ cm}}\) and the radius of its base is \(5{\text{ cm}}\) . The toy is painted red.
Calculate the length, \(l\), of the slant height of the cone.
Calculate the area that is painted red.
Markscheme
\(\sqrt {{5^2} + {{12}^2}} \) (M1)
Note: Award (M1) for correct substitution in Pythagoras Formula.
=\(13{\text{ (cm)}}\) (A1) (C2)
\({\text{Area}} = 2\pi {(5)^2} + \pi (5)(13)\) (M1)(M1)(M1)
Notes: Award (M1) for surface area of hemisphere, (M1) for surface of cone, (M1) for addition of two surface areas. Follow through from their answer to part (a).
\( = 361{\text{ c}}{{\text{m}}^2}\) (\(361.283 \ldots \)) (A1)(ft) (C4)
Note: The answer is \( 361{\text{ c}}{{\text{m}}^2}\) , the units are required.
