4400 Higher June 2009 Paper 3 Q16
16
Diagram NOT accurately drawn
A solid cone, P, has a base radius of 4 cm and a slant height of 9 cm.
(a) Calculate the total surface area of the cone.
Give your answer correct to 3 significant figures. (2)
Give your answer correct to 3 significant figures. (2)
Another solid cone, Q, is similar to P.
The base radius of Q is 6 cm.
The volume of Q is \(k\) times the volume of P.
(b) Calculate the value of \(k\). (2)
| Scheme | Marks |
|---|---|
| \(\pi \times 4^2 + \pi \times 4 \times 9\) | M1 |
| 163 | A1 |
| (2) |
Notes
A1: for ans rounding to 163
(\(\pi \to\) 163.3628... 3.14 \(\to\) 163.28 3.142 \(\to\) 163.384)
| Scheme | Marks |
|---|---|
\(\dfrac{6}{4}\) or 1.5 oe or 6 : 4 oe or \(\dfrac{4}{6}\) oe or 4 : 6 oe | M1 |
| 3.375 oe | A1 |
| (2) | |
| (4 marks) |
Notes
M1: May be implied by 13.5 or 12.09...
Also award for cube of any correct values or cube of correct ratios
A1: for 3.375 or \(3\frac{3}{8}\) or \(\frac{27}{8}\) oe
Accept 3.38 if M1 scored
Do not award A1 if slant heights used as \(h\) in \(V = \frac{1}{3}\pi r^2 h\)