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

Answer:

Option A . 1708 bags

Step-by-step 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

$V=\pi r^{2}h_1+\frac{1}{3}\pi r^{2}h_2$

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

$V=(3.14)(8)^{2}(16)+\frac{1}{3}(3.14)(8)^{2}(12)$

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

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

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

Answer 2

A

Trust me on this one too much to explain