Question
A cylinder is shown with a height of 4ft and diameter of 5ft is shown
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 ?
(1 point)
Responses
10π ft3
10π ft3
80π ft3
80π ft3
40π ft3
40π ft3
20π ft3
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 ?
(1 point)
Responses
10π ft3
10π ft3
80π ft3
80π ft3
40π ft3
40π ft3
20π ft3
Answers
GPT-4o mini
To find the volume of a cylinder (which represents the round bale of hay), you can use the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height.
Given:
- The diameter of the cylinder is 5 ft, so the radius \( r \) is half of that:
\[
r = \frac{5}{2} = 2.5 \text{ ft}
\]
- The height \( h \) is given as 4 ft.
Now plug these values into the formula:
1. Calculate \( r^2 \):
\[
r^2 = (2.5)^2 = 6.25
\]
2. Substitute \( r \) and \( h \) into the volume formula:
\[
V = \pi (6.25)(4) = 25\pi \text{ ft}^3
\]
Thus, the volume of the round bale of hay is \( 25\pi \) ft³.
From the options given, it seems like the correct choice is not listed. However, based on the calculation, the volume is \( 25\pi \) ft³. If you need to choose from the available options, it appears there may be a mistake in either the question or the options provided.
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height.
Given:
- The diameter of the cylinder is 5 ft, so the radius \( r \) is half of that:
\[
r = \frac{5}{2} = 2.5 \text{ ft}
\]
- The height \( h \) is given as 4 ft.
Now plug these values into the formula:
1. Calculate \( r^2 \):
\[
r^2 = (2.5)^2 = 6.25
\]
2. Substitute \( r \) and \( h \) into the volume formula:
\[
V = \pi (6.25)(4) = 25\pi \text{ ft}^3
\]
Thus, the volume of the round bale of hay is \( 25\pi \) ft³.
From the options given, it seems like the correct choice is not listed. However, based on the calculation, the volume is \( 25\pi \) ft³. If you need to choose from the available options, it appears there may be a mistake in either the question or the options provided.