1MA0 Higher March 2013 Paper 2 Q22
22
Diagram NOT accurately drawn
A frustrum is made by removing a small cone from a similar large cone.
The height of the small cone is 20 cm.
The height of the large cone is 40 cm.
The diameter of the base of the large cone is 30 cm.
Work out the volume of the frustrum.
Give your answer correct to 3 significant figures. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\frac{1}{3} \times \pi \times 15^2 \times 40\) \(- \frac{1}{3} \times \pi \times 7.5^2 \times 20\) | 8250 | 4 | B1 for 15cm as diameter or 7.5 cm as radius of smaller cone (may be marked on diagram or used in a formula) M1 for a numerical expression for the volume of one cone eg. \(\frac{1}{3} \times \pi \times 15^2 \times 40\) (=9424...) or \(\frac{1}{3} \times \pi \times 7.5^2 \times 20\) (=1178...) M1 for \(\frac{1}{3} \times \pi \times 15^2 \times 40\) oe − \(\frac{1}{3} \times \pi \times 7.5^2 \times 20\) oe A1 for answer in the range 8240 − 8250 OR B1 for \(2^3\) M1 for a numerical expression for the volume of the large cone eg. \(\frac{1}{3} \times \pi \times 15^2 \times 40\) (=9424...) M1 volume of frustrum = \(\frac{7}{8} \times \frac{1}{3} \times \pi \times 15^2 \times 40\) oe A1 for answer in the range 8240 − 8250 |