Higher June 2022 Unit 2 Q9
9. Calculate the total surface area of a solid hemisphere with a radius of 34 cm. [4]
Diagram not drawn to scale
Total surface area = …………… cm2
From the formula list: Surface area of sphere \(= 4\pi r^2\)
| Scheme | Marks | Comments |
|---|---|---|
| (Area of circular face=) \(\pi \times 34^2\ (= 1156\pi)\) | M1 | Accept values between 3629.8 and 3632.2 if \(\pi \times 34^2\) or \(1156\pi\) not seen. |
| (Curved surface area of hemisphere=) \(2 \times \pi \times 34^2\) o.e. | M2 | \(2312\pi\) or values between 7259·6 and 7264·4 M1 for sight of \(4 \times \pi \times 34^2\) or \(4624\pi\) or values between 14519 and 14529. Sight of \(3 \times \pi \times 34^2\) implies M1 M2. |
| (Total surface area=) 3468 π (cm2) or answers in the range: 10 889·4 (cm2) to 10 896·6 (cm2) | A1 | CAO. Mark final answer. Allow an answer of 10 900 from correct working. If no marks awarded, award SC2 for an unsupported \(5 \times \pi \times 34^2\) (\(5780\pi\) or values between 18 149 and 18 160·8). |