(a)[2]
A cuboid measures $x\text{ cm}$ by $x\text{ cm}$ by $10\text{ cm}$. Its volume is $62.5\text{ cm}^3$. Determine the value of $x$.
(b(i))[1]
A piece of card, $AOB$, forms a sector of a circle with centre $O$, angle $84^\circ$ and radius $15\text{ cm}$. Show that the arc length of the sector is $7\pi\text{ cm}$.
(b(ii))[2]
$OA$ is joined to $OB$ to create the curved surface of a cone. Calculate the radius of the cone.
(b(iii))[2]
Determine the height of the cone.
(c)[3]
An empty barrel, shaped like a cylinder, has radius $20\text{ cm}$ and height $80\text{ cm}$. Water enters the barrel at a rate of $5500\text{ cm}^3\text{/minute}$. Calculate how long it takes to fill the barrel completely. Give your answer in minutes and seconds, correct to the nearest second.