Question

A cylindrical bin with a diameter of 15 feet 3 inches and a height of 24 feet 4 inches is used to hold wheat on the farm where you're interning. One cubic foot holds 0.804 bushels. About how many bushels of wheat can be stored?

Answer 1

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`

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 = (Diameter)/(2)`

Radius = 7.63 feet

`\pi = 3.14`

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

Answer 2

3571.63 bushels

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.