Review question

# When is the volume of this pyramid a maximum? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9905

## Question

A right square pyramidal frame is formed from a rod of length $4a$ by dividing the rod into eight pieces, four being of length $x$ (to make the edges of the square base) and the other four of length $a - x$ (to make the sloping edges). The rods are jointed together without wastage. If the volume of the pyramid is $V$, and $x$ may vary, show that $\dfrac{dV}{dx} = 0$ when $x = 0$ and when $3x^2 - 10ax + 4a^2 = 0.$

Show that, when $x$ is equal to the smaller of the two roots of this equation,

1. a real pyramid can be formed,
2. $V$ has a maximum value.