4400 Higher November 2010 Paper 3 Q15
15 A solid is made from a cylinder and a hemisphere.
The cylinder has radius 1.5 cm and height 4 cm.
The hemisphere has radius 1.5 cm.
Diagram NOT accurately drawn
Work out the total volume of the solid.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\pi \times 1.5^2 \times 4\) (= 28.2...) | M1 |
| \(\frac{4}{3} \times \pi \times 1.5^3\) (= 14.1...) | M1 |
| “14.1” × 0.5 (= 7.06...) | M1 |
| cyl vol + hemisphere vol | M1 |
| 35.3 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: Volume of cylinder
M1: Volume of sphere
M1: 0.5 × their sphere vol
M1: dep M1M1
(allow cyl volume + sphere volume if hemisphere not calculated)
A1: 35.3 to 35.4 (not \(11.25\pi\))