The diagram shows a cuboid \(ABCDEFGH\).

\(AB = 7\) cm, \(AD = 14\) cm and \(BF = 22\) cm.

A box is in the shape of a cuboid measuring \(25\) cm by \(13\) cm by \(18\) cm.

Here is a cuboid.

Its base is a rectangle measuring \(6\) cm by \(14\) cm, and its height is \(h\) cm.

The distance from one corner of the cuboid to the opposite corner is \(31\) cm.

Work out the value of \(h\).

Relative to an origin \(O\), the point \(A\) has coordinates \((10,\ 21,\ 22)\) and the point \(B\) has coordinates \((13,\ 17,\ 10)\).

Calculate the length of \(AB\).

The diagram shows a cuboid \(ABCDEFGH\).

\(AB = 14\) cm, \(AD = 6\) cm and \(BF = 15\) cm.

Work out the size of the angle between \(AG\) and the base \(ABCD\).

Give your answer to 1 decimal place.

The diagram shows a solid pyramid \(ABCDV\).

The base \(ABCD\) is a square of side \(10\) cm. The vertex \(V\) is vertically above the centre of the base, and the perpendicular height of the pyramid is \(16\) cm.

All four sloping edges are the same length. One of them is marked \(x\).

The diagram shows a solid pyramid \(ABCDV\).

The base \(ABCD\) is a square of side \(20\) cm, and \(V\) is vertically above the centre of the base.

All four sloping edges are the same length, \(44\) cm.

Work out the perpendicular height of the pyramid.

Give your answer correct to 1 decimal place.

A solid pyramid \(ABCDV\) has a square base \(ABCD\) of side \(24\) cm.

\(V\) is vertically above the centre of the base, and the perpendicular height of the pyramid is \(46\) cm.

\(M\) is the midpoint of \(AB\).

Find the size of the angle between the face \(VAB\) and the base \(ABCD\).

Give your answer correct to 1 decimal place.

The diagram shows a solid triangular prism.

Each end of the prism is an isosceles triangle with a base of \(14\) cm and a perpendicular height of \(15\) cm. The prism is \(26\) cm long.

Three corners are marked. \(A\) is a bottom corner of one end, \(C\) is the top corner of that same end, and \(F\) is the top corner of the other end.

Find the length of \(AF\).

Give your answer to 1 decimal place.

On a moor, a vertical radio mast \(PQ\) stands on level ground. \(P\) is at the bottom and \(Q\) is at the top.

Two straight ropes run from \(Q\) to two anchors, \(A\) and \(B\), on the ground. \(A\), \(P\) and \(B\) do not lie in a straight line, so the two ropes are in different vertical planes.

\(QA = 25\) m and \(QB = 27\) m.

Rope \(QA\) makes an angle of \(36^\circ\) with the ground.

Work out the size of the angle rope \(QB\) makes with the ground.

Give your answer correct to the nearest degree.