Theory question 111
Mensuration of Solids(a) The diagram shows a pyramid standing on a cuboid. The dimensions of the cuboid are 4 m by 3 m by 2 m and the slant edge of the pyramid is 5 m. Calculate the volume of the shape.
(b) The 2nd, 3rd and 4th terms of an AP are x − 2, 5 and x + 2 respectively. Calculate the value of x.
Show the model answer
Model answer
(a) Cuboid volume = 4 × 3 × 2 = 24 m3.
Diagonal of the 4 m × 3 m top = √(16 + 9) = 5 m, half-diagonal = 2.5 m.
Pyramid height = √(52 − 2.52) = √18.75 ≈ 4.33 m.
Pyramid volume = ⅓ × 12 × 4.33 ≈ 17.32 m3.
Total ≈ 41.3 m3.
(b) Common difference: 5 − (x − 2) = (x + 2) − 5, so 7 − x = x − 3 and x = 5.
Explanation
The pyramid's vertex is above the centre of the top face, so use half the diagonal with Pythagoras.