1.
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\caption{Figure 1}
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A hollow toy is formed by joining a uniform right circular conical shell \(C\), with radius \(4 a\) and height \(3 a\), to a uniform hemispherical shell \(H\), with radius \(4 a\). The circular edge of \(C\) coincides with the circular edge of \(H\), as shown in Figure 1.
The mass per unit area of \(C\) is \(\lambda\) and the mass per unit area of \(H\) is \(k \lambda\) where \(k\) is a constant.
Given that the centre of mass of the toy is a distance \(4 a\) from the vertex of the cone, find the value of \(k\).