Core stretch A metal cube has side 4 m. Two rectangular pyramidal cavities, each with base \(1\text{

Question

Core stretch

A metal cube has side 4 m. Two rectangular pyramidal cavities, each with base $1\text{ m}\times2\text{ m}$ and height 2 m, are removed. Use $\pi=3.142$.

The cavities enter through opposite faces and meet only at their apex at the cube centre; their interiors do not overlap.

Find the remaining volume.[2]
Find its mass if density is $5400\text{ kg/m}^3$.[2]
It is recast as a solid hemisphere. Find
1. its radius to 3 s.f.,[2]
2. total surface area to 2 d.p.[2]

Accepted Answer

(a) $61.33\text{ m}^3$ (b) $331200$ kg (c)(i) $3.08$ m (ii) $89.55\text{ m}^2$.

A cube with two pyramidal cavities

A cube with two pyramidal cavities

Solution:

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