Question

Find the ratio of the edge of a cube to the radius of a sphere, if the volume of the cube is equal to the volume of the sphere.

• A. $1.61$
• B. $2.05$
• C. $2.33$
• D. $2.45$
• E. $2.65$

Answer 1

The correct option is A $1.61$

Let the length of edge of cube is $a$ and radius of sphere be $r$.
Volume of cube is $a^3$.
Volume of sphere is $\frac{4}{3}\times \pi r^3$
Given that both volumes are equal, so we get

${\left(\frac{a}{r}\right)}^3=\frac{4\pi }{3}=4.189$
$\therefore \frac{a}{r}=\sqrt[3]{34.189}=1.61$