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Mathematics · May / June 2025 · Paper 41 · Question 20

0580

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The question as text

NOT TO SCALE A Ğ O Ġ Ñ C 24 cm 10.5 cm 10.5 cm The diagram shows a pyramid OAÑCĞ. The pyramid has a square base, AÑCĞ, with sides 10.5 cm. The vertex O is vertically above the centre of the base, Ġ. The height of the pyramid is 24 cm.

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  • 20(a)[4]

    72.8 or 72.81… [4]

    M3 for 24 oe or better 1 10.5 2 + 2 10.5 2 1 10.5 2 + 2

    or M2 for AM = 10.5 oe 2 = or AM 10.5 cos45 oe

    or M1 for AC2 = 10.52 + 10.52 or AM 2 = 5.252 +5.252 AM 10.5 = or cos45 oe If 0 scored,

    SC1 for identifying ∠OAM

  • 20(b)[5]

    849 1 or 849 or 849.3… 3 [5]

    Method 1

    B2 for side of small square = 3.5

    or M1 for 10.5 24 = or better − x 24 16

    M2 for 1 3 × 10.52 × 24 – 1 3 × (their 3.5)2 × (24 – 16)

    or M1 for 1 3 × 10.52 × 24 or for 1 3 × (their 3.5)2 × (24 – 16) Method 2

    B2 for 1 27 or 26 27 − 3 24 16

    or M1 for volume scale factor = 24

    M2 for 1 1 − × × × 1 their 10.5 2 24 oe 27 3 1 10.5 3× 2 ×

    or M1 for 24 1 1 their × × 10.5 2 × 24 or oe 27 3

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