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CAIE IGCSE Mathematics Extended Solid Mensuration

Practise multi-step surface-area and volume problems involving linked dimensions, composite solids, conservation of material and equal-measure equations.

Syllabus
2028–2030
Course
Mathematics 0580
Level
Extended

Exam points

  • calculate a missing perpendicular height with Pythagoras before applying a solid formula
  • equate volumes or surface areas when material is recast or two solid measures are stated equal
  • combine unit conversion, flow or capacity information with a cuboid or curved-solid volume

Covered syllabus points

E5.4.1 Carry out calculations and solve problems involving the surface area

E5.4 Surface area and volume question 1

[Maximum number: 9]

Question (a)

(a)

A cylinder with radius 6 cm and height h cmh \mathrm{~cm} has the same volume as a sphere with radius 4.5 cm. Find the value of h.
[The volume, V, of a sphere with radius r is V=43πr3V=\frac{4}{3} \pi r^{3}.]

h=
[ 3 ]

Question (b)

(b)

A solid metal cube of side 20 cm is melted down and made into 40 solid spheres, each of radius r cmr \mathrm{~cm}.

Find the value of r.
[The volume, V, of a sphere with radius r is V=43πr3V=\frac{4}{3} \pi r^{3}.]

r=
[ 3 ]

Question (c)

(c)

A solid cylinder has radius x cmx \mathrm{~cm} and height 7x2 cm\frac{7 x}{2} \mathrm{~cm}.

The surface area of a sphere with radius R cmR \mathrm{~cm} is equal to the total surface area of the cylinder.
Find an expression for R in terms of x.
[The surface area, A, of a sphere with radius r is A=4πr2A=4 \pi r^{2}.]

R=
[ 3 ]
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