we know that
[volume of a cone]=pi*r²*h/3
r=14/2-----> r=7 in
slant height l=2 1/2 ft--------> l=2.5 ft
convert the slant height to in
1 ft-------> 12 in
2.5 ft-----> X
X=2.5*12------> X=30 in
l=30 in
the height of the cone is determined by using Pythagoras, since the cross section is a right triangle
l²=h²+r²--------> h²=l²-r²------> h²=30²-7²-----> h²=851
h=√851--------> h=29.17 in
[volume of a cone]=pi*r²*h/3------> pi*7²*29.17/3-----> 1496.13 in³
if the volume of a cone is 87% full
then
0.87*1496.13----------> 1301.63 in³
the answer is
the volume of a cone that is 87% full is 1301.63 in³