Given
A cylindrical bin with a diameter of 15 feet 3 inches and a height of 24 feet 4 inches is used to hold wheat.
One cubic foot holds 0.804 bushels
Find out bushels of wheat can be stored.
To proof
Formula
![Volume\ of\ a\ cylinder = \pi r^{2}h](https://tex.z-dn.net/?f=Volume%5C%20of%5C%20a%5C%20cylinder%20%3D%20%5Cpi%20r%5E%7B2%7Dh)
where r is the radius and h represent the height.
As given in the question
diameter = 15 feet 3 inches
height = 24 feet 4 inches
First convert inches into feet
I inches = 0.083 feet
15 feet 3 inches = 15 + 3 × 0.083
= 15.25 feet
Diameter = 15.25 feet
24 feet 4 inches = 24 + 4 ×0.083
= 24.33 feet
Height = 24.33 feet
![Radius\ of\ cylinder = \frac{Diameter}{2}](https://tex.z-dn.net/?f=Radius%5C%20of%5C%20cylinder%20%3D%20%5Cfrac%7BDiameter%7D%7B2%7D)
Radius = 7.63 feet
![\pi = 3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D%203.14)
Put all the value in the above formula.
we get
Volume of the cylinder = 3.14× 7.63× 7.63× 24.33
= 4447.55 foot³ ( approx)
As given
One cubic foot holds 0.804 bushels
Total bushels of wheat can be stored = 4447.55×0.804
= 3575.83 ( approx)
Total bhushels of wheat stored are 3575.83 ( approx).
Hence proved