Higher November 2018 Unit 2 Q12
12. Calculate the total surface area of a solid hemisphere with a base radius of 29 cm. [4]
Diagram not drawn to scale
From the formula list: Surface area of sphere \(= 4\pi r^2\)
Total surface area = …………………… cm2
| Scheme | Marks | Comments |
|---|---|---|
| (Curved surface area of hemisphere=) \(2 \times \pi \times 29^2\) o.e. | M2 | \(1682\pi\) or values between 5281.48 and 5284.844 M1 for sight \(4 \times \pi \times 29^2\) or \(3364\pi\) or values between 10562.96 and 10569.688. |
| (Area of base of hemisphere=) \(\pi \times 29^2\) | M1 | \(841\pi\) or values between 2640.7 and 2642.422 Sight of \(3 \times \pi \times 29^2\) implies M2 M1. |
| (Total surface area=) Answer in the range: 7922(cm2) to 7927.3(cm2) or 2523π (cm2) | A1 | CAO. Unsupported correct answer is awarded full marks. SC2 for an unsupported \(5 \times \pi \times 29^2\) (\(4205\pi\) or 13210.3…). |