Mathematics 0580 · IGCSE · Surface area and volume
Surface area and volume — practice question
A sphere of radius $r$ lies inside a closed cylinder with radius $r$ and height $2r$. [The volume, $V$, of a sphere with radius $r$ is $V = \frac{4}{3}\pi r^3$.]
(a(i))[3]
Calculate the volume of the region inside the cylinder that is not filled by the sphere.
(a(ii))[3]
Find $r$ when the volume inside the cylinder not occupied by the sphere is $36\text{ cm}^3$.
(b(i))[4]
Calculate the cost required to paint the cone.
(b(ii))[3]
Calculate how many smaller cones can be made.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct cylinder-and-sphere volume method” …