| Date | May 2018 | Marks available | 2 | Reference code | 18M.1.sl.TZ2.15 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
Julio is making a wooden pencil case in the shape of a large pencil. The pencil case consists of a cylinder attached to a cone, as shown.
The cylinder has a radius of r cm and a height of 12 cm.
The cone has a base radius of r cm and a height of 10 cm.
Find an expression for the slant height of the cone in terms of r.
The total external surface area of the pencil case rounded to 3 significant figures is 570 cm2.
Using your graphic display calculator, calculate the value of r.
Markscheme
(slant height2 =) 102 + r 2 (M1)
Note: For correct substitution of 10 and r into Pythagoras’ Theorem.
\(\sqrt {{{10}^2} + {r^2}} \) (A1) (C2)
[2 marks]
\(\pi {r^2} + 2\pi r \times 12 + \pi r\sqrt {100 + {r^2}} = 570\) (M1)(M1)(M1)
Note: Award (M1) for correct substitution in curved surface area of cylinder and area of the base, (M1) for their correct substitution in curved surface area of cone, (M1) for adding their 3 surface areas and equating to 570. Follow through their part (a).
= 4.58 (4.58358...) (A1)(ft) (C4)
Note: Last line must be seen to award final (A1). Follow through from part (a).
[4 marks]
