Mathematics 0580 · IGCSE · Surface area and volume

Surface area and volume — practice question

The diagram depicts a solid made by joining two hemispheres and a cylinder. The radius of the larger hemisphere is 5.4 cm. The radius of the smaller hemisphere and the radius of the cylinder are both 3.6 cm. The height of the cylinder is 6.5 cm.
(a(i))[4]

Show that the volume of the solid is $692\text{ cm}^3$, correct to the nearest cubic centimetre. [The volume, $V$, of a sphere with radius $r$ is $V = \frac{4}{3}\pi r^3$]

(a(ii))[4]

Calculate the total mass of this silver solid.

(b(i))[2]

Calculate the length of the arc of this sector. Give your answer as a multiple of $\pi$.

(b(ii))[4]

A cone is formed from this sector by joining OA to OB. Calculate the volume of the cone. [The volume, $V$, of a cone with radius $r$ and height $h$ is $V = \frac{1}{3}\pi r^2 h$]

Worked solution & mark scheme

This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: M1 for either \( \frac{2}{3}\pi(3.6)^3 \) or \( \frac{2}{3}\pi(5.4)^3 \)

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