Question 896848
Question (a):


volume of sphere, {{{v=(4/3)pi*r^3}}} 
volume of rectangular prism, in your case, {{{a*(a/2)*(a/4)=(1/8)a^3}}}.


You are given r=24 for the sphere,and that you want to find a for the prism being also this same volume.

{{{(1/8)a^3=(4/3)pi(24)^3}}}
Solve for a.
{{{a^3=8(4/3)pi(24)^3}}}
{{{a^3=2^5(1/3)pi(24)^3}}}
{{{a^3=2^8(1/3)pi}}}
{{{a=4root(3,4/3)root(3,pi)}}}
{{{highlight(a=4root(3,4pi/3))}}}


Try to do question (b) yourself.  Make the proper expression for the surface area of your prism; find the formula for surface area of a sphere in your book or other good reference material.