Question

How much grain can a farmer hold in this silo? Use π = 3.14.A. 2,093.3 ft³B. 11,513.3 ft³C. 9,420 ft³D. 12,560.2 ft³

Answer 1

To find out how much grain the farmer can hold we need to find the volume of the silo. The silo is made from a circular cylinder and half a sphere.

The volume of the cylinder is given by:

`V=\pi r^2h`

In this case r=10 and h=30, plugging this values in the equation above we have that the volume of the cylinder is:

`\begin{gathered} V=(3.14)(10)^2(30) \\ V=9420 \end{gathered}`

Hence the volume of the cylinder is 9420 cubic feet.

Now we need to find the volume ot half the sphere, the volume og an sphere is given by:

`V=(4)/(3)\pi r^3`

Plugging the radius we have that:

`\begin{gathered} V=(4)/(3)(3.14)(10)^3 \\ V=4186.6 \end{gathered}`

Now, we only need half this volume then the volume of the top of the silo is:

`V=2093.3`

Finally we add the volume of the cylinder and half the sphere, therefore the volume of the sylo is:

`11513.3`

and the answer is B.