Question 1163264
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The triangle (9,9,4) is an isosceles triangle.


Let "a" be its angle opposite to the base of "4".


Then  {{{sin(a/2)}}} = {{{2/9}}};  {{{a/2}}} = {{{arcsin(2/9)}}} = 0.2241 radians.


Hence, the angle  "a"  is  a = 2*0.2241 = 0.4482.


The number of such angles in full angle of  {{{2pi}}} radians is  {{{2pi/0.4482}}} = {{{(2*3.14)/0.4482}}} = 14.012,

or approximately 14.


Hence, the answer to the first question is 14 prisms.



Next, to find the volume of one such a prism, find first the area of its base.


To find the area of the  (9,9,4)-triangle, use the Heron's formula.


Semi-perimeter is  s = {{{(9+9+4)/2}}} = {{{22/2}}} = 11;

hence, the area is  A = {{{sqrt(s*(s-9)*s-9)*(s-4))}}} = {{{sqrt(11*2*2*7)}}} = {{{sqrt(308)}}} = 17.55 cubic inches.


The volume of one prism = 3*17.55 = 52.65 cubic inches,

and the volume of the 14 prisms is  14*52.65 = 737 cubic inches.    <U>ANSWER</U>
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Solved.