Higher June 2025 Paper 6 Q10
10 The diagram shows a sphere with radius 3 cm and a cube with side length \(x\) cm.
The surface area of the sphere is equal to the surface area of the cube.
Work out the side length, \(x\) cm, of the cube.
You must show your working.
[The surface area, \(A\), of a sphere with radius \(r\) is \(A = 4\pi r^2\).] [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\sqrt{6\pi}\) or 4.34… with correct working | 5 | Correct working requires evidence of at least M1 or B2 AND M1 or alternative method M2 | |
| B2 for \(36\pi\) or 113 to 113.143 or M1 for \(4\pi 3^2\) oe AND | |||
| M2 for \(\sqrt{\frac{\textit{their } 4\pi 3^2}{6}}\) or M1 for \(6x^2\) may be implied by div by 6 and square root | Their value must come from correct substitution into sphere formula \(\sqrt{\frac{\text{a positive value}}{6}}\) implies M1 \(\sqrt[3]{\frac{\text{a positive value}}{6}}\) implies M0 | ||
| If 0, 1 or 2 scored, instead award SC3 for \(\sqrt{6\pi}\) or 4.34… with no or insufficient working | |||
| Alternative method: M4 for \(\sqrt{\frac{4\pi 3^2}{6}}\) or better or M3 for \(\sqrt{\frac{4\pi r^2}{6}}\) or better or M2 for \(\frac{4\pi r^2}{6}\) or better or M1 for \(6x^2\) | After B2 scored, correct final answer from trials scores full marks Note: \(x^3 = 36\pi\) gives answer \(x\) = 4.84 (similar to correct answer 4.34) | ||