Mathematics 0580 · IGCSE · Surface area and volume
Surface area and volume — practice question
A cylinder partly filled with water is shown. A solid metal sphere is resting on the base of the cylinder, and half of the sphere is submerged in the water. The cylinder has radius 12 cm and the sphere has radius 3 cm.
(a)[3]
Show that $h = 0.125$. [For a sphere with radius $r$, the volume, $V$, is $V = \frac{4}{3}\pi r^3$.]
(b)[3]
Calculate $R$.
(c)[3]
Calculate the percentage of metal not used. [For a sphere with radius $r$, the volume, $V$, is $V = \frac{4}{3}\pi r^3$.]
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\pi \times 12^{2}h=\dfrac{1}{2} \times \dfrac{4}{3} \pi x^{3}$” …