Find the volume of the cone with vertex E and base circle through B,D,G.

01 / Standard#Your turn

Official paper · jm02-2026 · 1(c) · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The equal distances MB,MD,MG identify the circumcentre.

Hint 2

Use EM as the perpendicular height.

Worked solution

M is in the base plane and equidistant from its three vertices, so the radius is MG.
$r^2=MG^2=\frac23$
The body diagonal passes perpendicularly through the base centre.
$h=EM=\sqrt{3\left(\frac23\right)^2}=\frac{2\sqrt3}3$
Apply the cone-volume formula.
$V=\frac13\pi r^2h=\frac13\pi\frac23\frac{2\sqrt3}3=\frac{4\sqrt3\pi}{27}$

4√3π/27 cubic units.

Checks and common pitfalls: EC is the whole body diagonal, not the cone height EM.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
M is in the base plane and equidistant from its three vertices, so the radius is MG.
$r^2=MG^2=\frac23$
The body diagonal passes perpendicularly through the base centre.
$h=EM=\sqrt{3\left(\frac23\right)^2}=\frac{2\sqrt3}3$
Apply the cone-volume formula.
$V=\frac13\pi r^2h=\frac13\pi\frac23\frac{2\sqrt3}3=\frac{4\sqrt3\pi}{27}$

Think first. Reveal a hint when the class is ready.

2026 JM02