Answer:
[tex]d=10.0002\ inches[/tex]
Step-by-step explanation:
Given That:
Height=h=28 inches
Volume=V=732.7 cubic inches
Required:
Diameter of the base of the cone=d=?
Solution:
the formula for the volume of a cone is
[tex]V=\frac{1}{3}\pi\ r^{2}h[/tex]
re-arranging the terms to get the radius (r)
[tex]r^{2}= \frac{3V}{\pi h}\\r=\sqrt{\frac{3V}{\pi h}}[/tex]
putting values, we get
[tex]r=\sqrt{\frac{3(732.7)}{3.14(28)} }[/tex]
[tex]r=\sqrt{\frac{2198.1}{87.92} } \\r=\sqrt{25.001}\\ r=5.0001\ inches[/tex]
to find the diameter we know that diameter is double of the radius so[tex]d=2r\\d=2(5.0001)\\d=10.0002 \ inches[/tex]
