3D Pythagoras & Trigonometry Practice Questions

$ABCDEFGH$ is a cuboid.

$AB = 8$ cm, $BC = 6$ cm, $CG = 5$ cm.

Diagram not accurately drawn.

The diagram shows a fish tank in the shape of a cuboid $ABCDEFGH$ with a horizontal base $ABCD$.

$AB = 1.2$ m and $BC = 0.9$ m.

A straight rod fits exactly inside the tank from $A$ to $G$, so that $AG = 1.7$ m.

Diagram not accurately drawn.

The diagram shows a pyramid with a horizontal rectangular base $ABCD$.

$AB = 12$ cm and $BC = 9$ cm.

The vertex $T$ is vertically above $X$, the point where the diagonals of the base cross, and $TX = 10$ cm.

Diagram not accurately drawn.

$TABCD$ is a solid pyramid.

The base $ABCD$ is a horizontal square of side 16 cm.

$TA = TB = TC = TD = 17$ cm.

$M$ is the midpoint of $BC$.

Diagram not accurately drawn.

A marquee is made from vertical walls with a pyramid-shaped roof on top.

The base $PQRS$ of the marquee is a horizontal square of side 8 m.

The vertical walls are 2.5 m high.

The vertex $V$ of the roof is 3 m vertically above the centre of the top of the walls.

A straight support cable runs from the corner $P$ to the vertex $V$.

Diagram not accurately drawn.