Choosing spherical resin feedstock

Core stretch

A workshop sells spherical resin feedstock: small diameter 18 cm/$4.00, medium 24 cm/$6.80, and large 28 cm/$9.60. Use \(\pi=3.142\).

1. Show that a large sphere has volume \(11496\text{ cm}^3\) to 5 s.f.[2]
2. 1. How many complete \(320\text{ cm}^3\) castings can one large sphere supply?[2]
   2. A cylindrical mould has diameter 8 cm and its fill line is 1.2 cm below the rim. Find the mould height to 2 d.p.[2]
3. A $100 budget must supply resin for 250 castings.
   1. Determine the best value by volume per dollar.[2]
   2. Decide whether the budget suffices, ignoring waste.[2]