Shape and Space 9

In a cuboid, the length is 3 cm, the width is 4 cm, and the height is 5 cm. Work out the length of the space diagonal (the longest line from one corner to the opposite corner) to 1 decimal place.

In a square-based pyramid, each base edge is 6 cm and the vertex is 8 cm vertically above the centre of the base. Calculate, to 3 significant figures, the length of the slope from a corner of the base to the vertex.

Explain how to use Pythagoras’ theorem to calculate the direct distance from one corner of a cuboid to the opposite corner (the space diagonal).

A triangular prism has a right-angled triangle as its cross-section with side lengths 5 cm, 12 cm and 13 cm. The prism is 8 cm long.

The table below shows the lengths (in cm) of the edges of three different cuboids.

Work out the length of the longest space diagonal for each cuboid, giving your answers to 1 decimal place.

The diagram below shows a cuboid ABCDEFGH with AB = 4 cm, BC = 5 cm, and BF = 12 cm.

Work out the length of the space diagonal AE.

A pyramid has a square base PQRS, with PQ = QR = 6 cm. The vertex T is vertically above the centre of the base TSQ. The height VT = 9 cm.

Calculate the length of the edge VP from the vertex to a base corner.

A cuboid has dimensions 6 cm × 8 cm × 10 cm. Using Pythagoras’ theorem, explain how to find the length of its longest diagonal.

The diagram shows a rectangular box. The base AB = 9 cm, BC = 5 cm, and the height is BE = 12 cm. Point F is directly above C.

For a square-based pyramid with base edge of 10 cm and height of 15 cm (vertex directly above the centre), work out the vertical angle (angle between a side face and the base).