3D Pythagoras & Trigonometry Quiz

1. A cuboid has edges 3 cm, 4 cm and 12 cm. What is the length of its space diagonal?

• A. 13 cm
• B. 19 cm
• C. $\sqrt{19}$ cm
• D. 169 cm

2. In cuboid $ABCDEFGH$ (base $ABCD$, $E$ above $A$, $F$ above $B$, $G$ above $C$, $H$ above $D$), which base vertex lies directly below $G$?

• A. $A$
• B. $B$
• C. $C$
• D. $D$

3. A cuboid has base diagonal 10 cm and height 6 cm. What is the angle between the space diagonal and the base plane, to 1 d.p.?

• A. $59.0^{\circ}$
• B. $30.9^{\circ}$
• C. $31.0^{\circ}$
• D. $36.9^{\circ}$

4. Which pair of lengths forms the two legs of the right-angled triangle used to find the angle between a cuboid's space diagonal and its base plane?

• A. The base diagonal and the vertical height
• B. Two side edges of the base
• C. The space diagonal and a side edge
• D. Two vertical edges

5. A cuboid has $l = 5$ cm, $w = 5$ cm, $h = 2$ cm. Find the angle between the space diagonal and the base plane, to 1 d.p.

• A. $15.9^{\circ}$
• B. $74.1^{\circ}$
• C. $21.8^{\circ}$
• D. $19.6^{\circ}$