4400 Higher June 2007 Paper 3 Q18
18
Diagram NOT accurately drawn
A solid hemisphere A has a radius of 2.8 cm.
(a) Calculate the total surface area of hemisphere A.
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
A larger solid hemisphere B has a volume which is 125 times the volume of hemisphere A.
(b) Calculate the total surface area of hemisphere B.
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
| Scheme | Marks |
|---|---|
| \(\pi \times 2.8^2 + \frac{1}{2} \times 4\pi \times 2.8^2\) | M2 |
| 73.9 | A1 |
| (3) |
Notes
M2: M1 for each term
Also award for values rounding to 24.6 and to 49.2 or 49.3
A1: for 73.9 or for answer which rounds to 73.9
| Scheme | Marks |
|---|---|
| \(\sqrt[3]{125}\) or 5 seen | M1 |
| \(25 \times 73.89...\) | M1 |
| 1850 | A1 |
| (3) | |
| (6 marks) |
Notes
M1: for 25 × (a)
or for \(\pi \times (2.8 \times 5)^2 + 2\pi \times (2.8 \times 5)^2\)
or for substituting \(r = 2.8 \times 5\) in the expression used in (a)
A1: for 1850 or for any value in range 1846.3 − 1847.5
ft from 25 × (a)