Mathematics · Oct / Nov 2025 · Paper 41 · Question 14
0580
As printed in the paper
The question as text
A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is 8 cm.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
14(a)[1]
[= 256 π 4 3 ×× π 4 3 ] 3 [1]
14(b)[3]
47.6 nfww or 47.63 to 47.64… nfww [3]
B2 for 52.4 or 52.35 to 52.37 or 50 π nfww 3 OR 256 3 − π 8 3 ×
M2 for 100 oe 3 8 256 π 256 − π 8 3 3 3
or M1 for [ 100] × oe or × 100 8 3 8 3 oe
14(c)[2]
2.11 or 2.107… [2]
M1 for 256 π 7.86 × 3
14(d)[4]
233 or 233.3 to 233.4 [4]
M1 for 256 π 3.1 π × 2 × = h 3 × π × 3.1 2 + × 2 π × 3.1 their h × M2dep for 2 or M1dep for 2 π 3.1 theirh ×× × 2π
or M1 for × 3.1 2
Make a free account to save your answers and see your weak topics and ask the AI why a wrong answer is wrong.