ANSWER :
a. 628 cubic foot
b. 52 cubic foot
c. 1.17 ton
EXPLANATION :
The volume formula of a cylinder is :
[tex]V=\pi r^2h[/tex]
The volume formula of a cone is :
[tex]V=\frac{1}{3}\pi r^2h[/tex]
From the problem, we have a diameter of 10 ft, so the radius is r = 5 ft
Cylinder's height is 8 ft and cone's height is 2 ft
a. volume of cylinder part :
[tex]\begin{gathered} V=\pi(5)^2(8) \\ V=628ft^3 \end{gathered}[/tex]
b. volume of cone part :
[tex]\begin{gathered} V=\frac{1}{3}\pi(5)^2(2) \\ V=52ft^3 \end{gathered}[/tex]
c. The combine volume is 628 + 52 = 680 cubic foot
A dry corn weighs 45 lbs per cubic foot.
That will be :
[tex]52ft^3\times\frac{45lbs}{ft^3}=2340lbs[/tex]
There are 2000 pounds per ton, so that will be :
[tex]2340lbs\times\frac{1ton}{2000lbs}=1.17ton[/tex]
