The diagram shows a metal buoy. It is made up of a cone and a hemisphere. The cone is mounted on the base of a hemisphere with a radius of 0.6 m.
Given that the slant height of the cone is 1 m,
show that the height of the buoy is 1.4 m.[1]
calculate the total surface area of the buoy.[3]
calculate the volume of the buoy, leaving your answer in terms of \(\pi\).[3]
The buoy shown in Figure 1 is melted and recast into the prism shown below. The prism has height 1.5 m, and its cross-section is the sector \(OAB\), where angle \(AOB\) is \(\dfrac{11\pi}{30}\) radians. Assuming no material is lost during the recasting process, find the radius of the sector.[4]