Foundation June 2025 Paper 1 Q15
15
(a) A sphere has diameter 20 cm
Show that the radius of the sphere is 10 cm [1 mark]
(b) The volume of a sphere is \(\dfrac{4}{3}\pi r^3\) where \(r\) is the radius.
Work out the volume of a sphere with diameter 20 cm
Give your answer in terms of \(\pi\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(20 \div 2\ (= 10)\) | B1 | oe eg you halve it |
Additional guidance
| Ignore any attempt to find an area or volume | |
| \(r\) is half of \(d\) | B1 |
| \(d\) is double \(r\) | B1 |
| \(10 \times 2\ (= 20)\) | B1 |
| \(20 - 10 = 10\) | B0 |
| Radius is smaller than diameter | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(10^3\) or \(10 \times 10 \times 10\) or 1000 | M1 | [1300, 1334] or [3100, 3142] or [4030, 4192] implies 1000 |
| \(\dfrac{4000}{3}\pi\) | A1 | oe in terms of \(\pi\) condone a multiplication sign SC1 \(\dfrac{32\,000}{3}\pi\) |
Additional guidance
| SC1 is from using diameter instead of radius | |
| Accept 1333(. …) for \(\dfrac{4000}{3}\) | |
| \(4000\pi \div 3\) (1000 implied) | M1A0 |
| Ignore simplification or conversion attempts after correct answer |