Mathematics 4024 · O Level · Pythagoras' theorem and trigonometry in 3D
Pythagoras' theorem and trigonometry in 3D — practice question
The diagram depicts a pyramid $ABCV$. Its base is the equilateral triangle $ABC$, with each side measuring $34\text{ cm}$. The perpendicular height $VO$ meets the base at right angles. Also, $VA = VB = VC = 82\text{ cm}$.
(a)[1]
State the number of planes of symmetry of the pyramid.
(b(i))[3]
Use that $M$ is the midpoint of $AC$. The ratio $MO:OB$ is $1:2$. Show that $OB = 19.6\text{ cm}$, correct to $1$ decimal place.
(b(ii))[2]
Calculate the angle formed by the edge $VB$ and the base of the pyramid.
(b(iii))[5]
Calculate the pyramid's volume.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “3” …