Respuesta :
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
[tex]Volume\ of\ a\ cylinder = \pi r^{2}h[/tex]
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
[tex]Radius\ of\ cylinder = \frac{Diameter}{2}[/tex]
Radius = 7.63 feet
[tex]\pi = 3.14[/tex]
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
Answer:
3571.63 bushels
Step-by-step explanation:
The volume of a cylinder is found using the formula
V = πr²h
For our cylinder, h, the height, is 24 feet 4 inches. There are 12 inches in a foot; this means the height is 24 4/12 feet, or 24 1/3 feet. Writing this as an improper fraction, h = 73/3.
The diameter of our cylinder is 15 feet 3 inches. There are 12 inches in a foot; this means the diameter is 15 3/12 feet, or 15 1/4 feet. Writing this as an improper fraction, d = 61/4.
The radius is 1/2 of the diameter; this means r = 61/4(1/2) = 61/8.
Using these in our formula and using 3.14 for π, we have
V = 3.14(61/8)²(73/3) = 4442.33 ft³
Each cubic foot holds 0.804 bushels of wheat; this means the cylindrical bin can hold
4442.33(0.804) = 3571.63 bushels.
