Mathematics 0580 · IGCSE · Circles, arcs and sectors
Circles, arcs and sectors — practice question
The diagram illustrates a cross section of a cylinder with centre $O$ and radius $r$, resting on its side.
Water in the cylinder reaches a depth of $18\text{ cm}$.
The width, $AB$, across the water surface is $24\text{ cm}$.
(a)[4]
Use an algebraic approach to show that $r = 13\text{ cm}$.
(b)[2]
Show that angle $AOB = 134.8^\circ$, accurate to 1 decimal place.
(c(i))[3]
Calculate the area enclosed by the major sector $OAPB$.
(c(ii))[3]
Calculate the area of shaded segment $APB$.
(c(iii))[1]
Calculate the volume of water inside the cylinder.
(d)[2]
Find the value of $h$.
Worked solution & mark scheme
This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Try to use $18 - r$ in Pythagoras” …