Choosing spherical resin feedstock

Choosing spherical resin feedstock

Secondary 2
TGM Original Questions

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.
    1. How many complete \(320\text{ cm}^3\) castings can one large sphere supply?
    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.
  3. A $100 budget must supply resin for 250 castings.
    1. Determine the best value by volume per dollar.
    2. Decide whether the budget suffices, ignoring waste.

Solution:

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Answer:(a) \(11496\text{ cm}^3\); (b)(i) \(35\) castings; (ii) \(7.57\) cm; (c)(i) large; (ii) yes—7 large spheres cost \(\$67.20\).

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