Once there were cubes and spheres

Geometry Level 4

A sphere and a cube have the same surface area. If the ratio of the volume of the cube to the sphere can be expressed in the form

$\left(\frac {A}{B}\right)^{n}$

where $A = \pi$ , $B$ is an integer, and $n$ is rational, find the value of $A+B+n$ .

1 solution

Mehul Arora
Feb 18, 2016

$4 \pi r^2= 6s^2$

$s = 2r \sqrt {\dfrac {\pi}{6}}$

Volume of sphere = $\dfrac {4}{3} \pi r^3$

Volume of cube = $s^3= 8r^3 \dfrac {\pi}{6}^{(\dfrac {3}{2})}$

$\dfrac {V_{cube}}{V_{sphere}}= \dfrac {\pi}{6} ^ {(\dfrac {1}{2})}$

$a+b+n= 3.14+6+0.5 = 9.64$

Solved in the same way.

Niranjan Khanderia - 5 years, 3 months ago