Question

A grain bin is in the combined shape of a right cylinder and right cone, both of which have diameters of 10 feet.(a) Find the volume of the cylindrical portion of the bin to the nearest cubic foot.(b) Find the volume of the conical portion of the bin to the nearest cubic foot.(c) The bin is to be filled completely with dry corn that weighs 45 lbs per cubic foot. Of there are 2,000 pounds per ton, how many total tons of corn can be placed in the bin?

Answer 1

a. 628 cubic foot

b. 52 cubic foot

c. 1.17 ton

EXPLANATION :

The volume formula of a cylinder is :

`V=\pi r^2h`

The volume formula of a cone is :

`V=(1)/(3)\pi r^2h`

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 :

`\begin{gathered} V=\pi(5)^2(8) \\ V=628ft^3 \end{gathered}`

b. volume of cone part :

`\begin{gathered} V=(1)/(3)\pi(5)^2(2) \\ V=52ft^3 \end{gathered}`

c. The combine volume is 628 + 52 = 680 cubic foot

A dry corn weighs 45 lbs per cubic foot.

That will be :

`52ft^3*(45lbs)/(ft^3)=2340lbs`

There are 2000 pounds per ton, so that will be :

`2340lbs*(1ton)/(2000lbs)=1.17ton`