Question 941502
let r1 be the radius of cone p
let r2  be the radius of cone q
volume of cone p = 840 cm^3
volume of cone q  =one  third of volume of cone p
           = 840/3
         = 280 cm^3
Formula : volume of cone  V ={{{(1/3)*pi*r^2*h}}}
                   {{{ 840 = (1/3)*pi*r1^2*h}}}
                     multiply with 3 on both sides
 {{{ 840*3 =(1/3)*3*pi*r1^2*h}}}
{{{2520= pi*r1^2*h}}}..............eq(1)

 similarly for cone q
                {{{ 280 = (1/3)*pi*r2^2*h}}}
             [[[ 280*3 = pi*r2^2*h}}}
           {{{840 =pi*r2^2*h}}}..............eq(2)
  divide eq(1) with eq(2)
{{{ 2520/840 =(pi*r1^2*h)/(pi*r2^2*h)}}}
 {{{ 3= r1^2/r2^2}}}
  {{{ (r1/r2)^2 = 3}}}
     {{{ r1/r2 =sqrt(3)}}}
      {{{r1/r2=1.73}}}
 r1= 1.73*r2
radius of cone p = 1.73  time  radius of cone q
 diameter  = 2* radius
the above rule applicable to diameter also
Result : diameter of cone  p =1.73 times the diameter of cone q