(a)[3]
The diagram depicts a sphere enclosed by a cube. The sphere is touching all 6 faces of the cube. The cube’s volume is $343\text{ cm}^3$. Calculate the volume of the sphere. (Volume of sphere $= \frac{4}{3}\pi r^3$)
(b)[2]
Solid $A$ is mathematically similar to solid $B$. Solid $A$ has volume $540\text{ cm}^3$ and height $15\text{ cm}$. Solid $B$ has volume $1280\text{ cm}^3$. Calculate the height of solid $B$.
(c)[5]
The diagram shows a solid made by joining a cone to a cylinder. The cone and the cylinder both have radius $6.3\text{ cm}$. The slant height of the cone is $8.7\text{ cm}$. The ratio height of cone : height of cylinder $= 2 : 3$. Calculate the total surface area of the solid. (Curved surface area of cone $= \pi r l$)