Question

A grain silo is approximately 85% full. A 55 lb sack of grain measures 2 cubic feet.

What is the best estimate of the number of bags of grain that can be filled using all the grain in the silo?
A
1708 bags

B
2010 bags

C
6833 bags

D
8038 bags

Answer 1

A

Trust me on this one too much to explain

Answer 2

Option A . 1708 bags

Explanation:

The picture of the question in the attached figure

step 1

Find the volume of the silo

The volume of the silo is equal to the volume of a cylinder plus the volume of a cone

so

`V=\pi r^(2)h_1+(1)/(3)\pi r^(2)h_2`

we have

`\pi =3.14`

`r=16/2=8\ ft` ---> the radius is half the diameter

`h_1=16\ ft`

`h_2=12\ ft`

substitute

`V=(3.14)(8)^(2)(16)+(1)/(3)(3.14)(8)^(2)(12)`

`V=3,215.36+803.84=4,019.2\ ft^3`

Remember that

The silo is approximately 85% full

so

The volume of grain in the silo is

`0.85(4,019.2)=3,416.32\ ft^3`

step 2

Find the number of bags of grain

Divide the volume of grain in the silo by the volume of one sack

`3,416.32/2=1,708\ bags`