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Edexcel IGCSE Math B 7.C 3D mensuration Question Bank

Practise volume and surface area of 3D solids, including cylinders, cones, hemispheres, prisms and compound objects in diagrams.

Syllabus
First assessment 2018
Course
Math B 4MB1

Exam points

  • calculate empty space by subtracting sphere or cone volumes from a cuboid or compound solid
  • find total surface area by selecting exposed circular, curved and rectangular faces
  • use a given volume or ratio to solve for r, h or a surface-area expression

7.C 3D mensuration question 1

[Maximum number: 2]
Figure for Question 7.C 3D mensuration question 1 — Edexcel IGCSE Math B
Figure for Question 7.C 3D mensuration question 1 — Edexcel IGCSE Math B

Diagrams NOT accurately drawn.

Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid, in the shape of a cuboid, shown in Figure 4.
The volume of the box is V cm3V\,\mathrm{cm}^3.

Show that V=4x3−60x2+200xV=4 x^{3}-60 x^{2}+200 x

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