Spherical cargo pod and crane payload

Spherical cargo pod and crane payload

Secondary 2
TGM Original Questions

A spherical exhibition cargo pod has internal volume \(2400\text{ m}^3\). Its shell, frame and instruments have masses 85 kg, 70 kg and 35 kg. Two full coolant tanks together have mass 160 kg; each contains 45 L of coolant of density \(800\text{ kg/m}^3\). Use \(\pi=3.142\).

  1. Find the pod radius to 3 d.p.
  2. Find its surface area to 2 d.p.
  3. Express the coolant volume in each tank in cubic metres.
  4. Find each empty tank mass.
  5. A crane can lift 900 kg and each display crate has mass 70 kg. Find the maximum number of crates lifted with the pod and full tanks.

Solution:

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Answer:(a) \(8.305\) m; (b) \(866.92\text{ m}^2\); (c) \(0.045\text{ m}^3\); (d) \(44\) kg; (e) \(7\) crates.

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