Mathematics 4024 · O Level · Surface area and volume

Surface area and volume — practice question

The diagram depicts a pentagon. Every length is given in centimetres.
(a(i))[2]

Calculate the area of the pentagon.

(a(ii))[3]

Determine the perimeter of the pentagon.

(b)[3]

A sphere’s volume is $\frac{4}{3}\pi r^3$. A sphere has a volume of $2572\text{ cm}^3$. Find the radius of the sphere.

(c(i))[3]

A cuboid measures $2\text{ cm}$ by $6\text{ cm}$ by $22.5\text{ cm}$. Calculate the surface area of the cuboid.

(c(ii))[3]

A cube with edge $x\text{ cm}$ has the same surface area as the cuboid. Write an equation in $x$ and solve it to determine the length of the cube’s edge.

Worked solution & mark scheme

This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: Calculation of area

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI