Question

In Figure 2, $d$ is the distance from vertex $F$ to vertex $G$. the base is square and the height is twice the width. Calculate the volume of the solid in terms of $d$.

• A. $12d^3\sqrt{6}$
• B. $10d^3\sqrt{5}$
• C. $\frac{d^3\sqrt{6}}{18}$
• D. $\frac{2d^3\sqrt{5}}{25}$

Answer 1

The correct option is C $\frac{d^3\sqrt{6}}{18}$

Let the length of side of base be $a$, then height will be $2a$
$\Rightarrow d=\sqrt{{\left(2a\right)}^2+{\left(\sqrt{2}a\right)}^2}=\sqrt{6a^2}=\sqrt{6}a$

$\Rightarrow a=\frac{d}{\sqrt{6}}$
$\therefore$ volume of solid is $a\times a\times 2a=2a^3=2{\frac{d}{\sqrt{6}}}^3=\frac{d^3}{3\sqrt{6}}$