What is the volume of a cone that is 87% full, has a diameter of 14 inches and a slant height of 2 and 1/2 feet.

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

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