Question 612061
The height of the cylinder (h) is three time the diameter of each ball, or:
{{{h = 3(13)}}}cm.
{{{h = 39}}}cm.
The radius of the cross-section of the cylinder is the same as the radius of a ball, or:
{{{r = 13/2}}}
{{{r = 6.5}}}cm.
a) The volume of the cylinder is:
{{{V[c] = (pi)r^2*h}}} Substitute {{{r = 6.5}}},{{{h = 39}}} and use {{{pi = 3.14}}} as an approximation.
{{{V[c] = (3.14)(6.5)^2(39)}}}
{{{V[c] = 5173.935}}}cu.cm. Round to nearest cubic cm. to get:
{{{V[c] = 5174}}}cu.cm.
b) The total volume of the three balls is:
{{{V[b] = 3(4/3)(pi)r^3}}} 
{{{V[b] = 4(3.14)(6.5)^3}}}
{{{V[b] = 3449.29}}}cu.cm. Round the nearest cubic cm. to get:
{{{V[b] = 3449}}}cu.cm.
c) The percent volume of the container occupied by the three balls is:
{{{V = (3449/5174)*100}}}
{{{V = 66.66%}}}%