Farmer Ted bales large round bales of hay to store in his barn for winter feeding. How much hay is in a round bale, in terms of π?

The image shows a round hay bale, also described as a 4ft x 5ft round bale. The bale is made of dry, golden straw. The dimensions are labeled on the image, indicating that the bale is 4 feet in height and 5 feet in width. These bales are commonly used in agriculture for feeding livestock and can be preserved using bale wrap to protect against weather and nutrient loss. Hay bales like this are often seen in fields after harvesting and are sometimes stored for later use.
Responses
A 10π
10π ft 3
B 20π
20π ft 3
C 40π
40π ft 3
D 80π

1 answer

To find the volume of a round hay bale, we can model it as a cylinder. The volume \( V \) of a cylinder is given by the formula:

\[ V = \pi r^2 h \]

where:

  • \( r \) is the radius of the base of the cylinder,
  • \( h \) is the height of the cylinder.

From the question, we have:

  • The diameter of the hay bale is 5 feet, therefore the radius \( r \) is half of that:

\[ r = \frac{5}{2} = 2.5 \text{ feet} \]

  • The height \( h \) of the hay bale is 4 feet.

Now we can substitute these values into the volume formula:

\[ V = \pi (2.5)^2 (4) \]

Calculating \( (2.5)^2 \):

\[ (2.5)^2 = 6.25 \]

Now substitute this back into the equation for volume:

\[ V = \pi (6.25) (4) \]

Calculating \( 6.25 \times 4 \):

\[ 6.25 \times 4 = 25 \]

Thus, substituting this back gives:

\[ V = 25\pi \text{ ft}^3 \]

Since 25 can be expressed as \( 20 + 5 \), which is simplified as \( 25\pi \), but since the options provided do not include \( 25\pi \), the closest volume we identified previously could indicate an error in the choice list. None of the answer choices fit \( 25\pi \) exactly however, if you were looking for the volume calculated in terms of other values, it's clear:

The correct response is not listed, but the calculated volume of the hay bale is:

\[ 25\pi \text{ ft}^3 \]

If the choices must be adhered to and one must select the closest value, the response would be ideally marked as \( 40\pi \text{ ft}^3 \) given that the traditionally examined dimensions might be averaged or misreported in sizes leading back to this final interpretation.