CAIE IGCSE Mathematics Extended E6.6.1 In 3d Carry Out Calculations and Solve Problems in Three Dimensions Questions

Practise Extended CAIE IGCSE Mathematics by deriving face or cross-section diagonals, projecting lines onto planes, and applying Pythagoras or trigonometric ratios to three-dimensional problems.

Exam points

Calculate a face or cross-section diagonal with Pythagoras before using it in a second three-dimensional triangle.
Identify the projection of a line onto a plane when finding the angle between the line and that plane.
Use Pythagoras or a trigonometric ratio in the derived 3D triangle and keep intermediate values accurate.

[Maximum number: 4]

NOT TO SCALE

ABCDEFGH is a cuboid with a square base of side $x \mathrm{~cm}$ . $C G=20 \mathrm{~cm}$ and $A G=28 \mathrm{~cm}$ .

Calculate the value of x.

13.9 or 13.85 to 13.86
M3 for $2x^2=28^2-20^2$ or better, or M2 for $x^2+x^2+20^2=28^2$ , or M1 for any correct Pythagoras in 2D or their $AC\times\sin45^\circ$

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CAIE IGCSE Mathematics Extended E6.6.1 In 3d Carry Out Calculations and Solve Problems in Three Dimensions Questions question 1