2025 IGCSE 0580 May/June P21 Q13

The diagram shows solid \(A\) and solid \(B\).

Solid \(A\) is made from a hemisphere and a cone each with radius \(6\text{ cm}\).

The cone has sloping edge \(10\text{ cm}\).

Solid \(B\) is a cylinder with radius \(4\text{ cm}\) and height \(h\text{ cm}\).

The total surface area of solid \(A\) is equal to the total surface area of solid \(B\).

1. Work out the value of \(h\).[5]
2. Work out the height of solid \(A\).[3]