Spherical cargo pod and crane payload

Core stretch

A spherical exhibition cargo pod has external volume \(24\text{ m}^3\). Its shell, frame and instruments have masses 85 kg, 70 kg and 35 kg. Two identical full coolant tanks together have mass 160 kg; each contains 45 L of coolant of density \(800\text{ kg/m}^3\). Use \(\pi=3.142\).

Treat the stated component masses as the complete pod mass, including contained air. The tanks are attached externally.

1. Find the pod radius to 3 d.p.[2]
2. Find its surface area to 2 d.p.[2]
3. Express the coolant volume in each tank in cubic metres.[2]
4. Find each empty tank mass.[2]
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.[2]