Foundation June 2025 Paper 3 Q21
21 The diagram shows a sphere with radius \(r\) cm.
The sphere has a circumference of 50 cm.
Work out the surface area of the sphere.
[The surface area, \(A\), of a sphere with radius \(r\) is \(A = 4\pi r^2\).] [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 796 or 795.67 to 796.4 | 4 | M2 for [\(r =\)] \(\dfrac{50}{2\pi}\) oe or B2 for 7.96 or 7.956 to 7.958 or M1 for \(2\pi r = 50\) oe | Accept \(\dfrac{2500}{\pi}\) or 253.3[...]\(\pi\) for 4 marks May be \(50 \div \pi \div 2\) or \(25 \div \pi\) Note \(\dfrac{50}{2\pi} = 7.956 \approx 8\) then \(4 \times \pi \times 8^2\) scores M2 M1 A0 |
| and M1 for \(4 \times \pi \times (\textit{their}\ r)^2\) oe or \(4 \times \pi \times \left(\dfrac{50}{2\pi}\right)^2\) oe | For M1 substitution of their r must be explicit Their r may be any value from 3 to 10 understood to be their radius \(\pi\) may be substituted with 3.142 or calculator value, allowing 3.14 and \(\dfrac{22}{7}\) | ||