Question

A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below:
http://prntscr.com/a7201k

Which of the following could be used to calculate the total volume of grains that can be stored in the silo?

π(8.5ft)2(2ft) + one over threeπ(2ft)2(13ft − 8.5ft)
π(2ft)2(8.5ft) + one over threeπ(2ft)2(13ft − 8.5ft)
π(8.5ft)2(2ft) + one over threeπ(13ft − 8.5ft)2(2ft)
π(2ft)2(8.5ft) + one over threeπ(13ft − 8.5ft)2(2ft)

I know the formula for finding the volume of a cone but I can't get further than that. The question itself confuses me and looking at the answer choices confuses me even more. I'm not sure what to do at all with this.

Answer 1

@johnweldon1993

Answer 2

Break up the composite figure into 2 shapes

A cylinder and a cone



Volume of a cylinder: \(\large \pi r^2 h\)
Volume of a cone: \(\large \frac{1}{3}\pi r^2 h\)

So since those 2 shapes are together, just add the corresponding volumes

\[\large V_T = V_{cylinder} + V_{cone} = \pi (2ft)^2 8.5ft + \frac{1}{3} \pi (2ft)^2 (13ft - 8.5ft)\]

Answer 3

Dont ever look at the whole thing at once :) Break it into parts

Like you said, you knew the volume equation for the cone...and the dimensions gave you the radius and the height...so it was easy to find out!

Answer 4

So where do we get the (13 ft - 8.5 ft) from?

Answer 5

That is the height of the cone

Notice how they give you the whole height of the entire silo