Question
Which expression can be used to find the height of the cone below?
A cone with base of 8 feet squared and volume of 30 feet cubed.
30 = one-third (8 h)
8 = 30 h
30 = 8 h
8 = one-third (30 h)
A cone with base of 8 feet squared and volume of 30 feet cubed.
30 = one-third (8 h)
8 = 30 h
30 = 8 h
8 = one-third (30 h)
Answers
Answered by
GPT-4o mini
To find the height of a cone given the base area and volume, you can use the formula for the volume of a cone:
\[
V = \frac{1}{3}Bh
\]
where \( V \) is the volume, \( B \) is the base area, and \( h \) is the height.
In your case, the volume \( V \) is 30 cubic feet and the base area \( B \) is 8 square feet. Plugging these values into the formula gives:
\[
30 = \frac{1}{3}(8)h
\]
To eliminate the fraction, you can multiply both sides by 3:
\[
90 = 8h
\]
Now, to solve for \( h \), you would divide both sides by 8:
\[
h = \frac{90}{8} = 11.25
\]
Considering the original question which expression can be used to find the height of the cone, the correct expression is:
\[
30 = \frac{1}{3}(8)h
\]
So, the correct answer from the options you've provided is:
**30 = one-third (8 h)**.
\[
V = \frac{1}{3}Bh
\]
where \( V \) is the volume, \( B \) is the base area, and \( h \) is the height.
In your case, the volume \( V \) is 30 cubic feet and the base area \( B \) is 8 square feet. Plugging these values into the formula gives:
\[
30 = \frac{1}{3}(8)h
\]
To eliminate the fraction, you can multiply both sides by 3:
\[
90 = 8h
\]
Now, to solve for \( h \), you would divide both sides by 8:
\[
h = \frac{90}{8} = 11.25
\]
Considering the original question which expression can be used to find the height of the cone, the correct expression is:
\[
30 = \frac{1}{3}(8)h
\]
So, the correct answer from the options you've provided is:
**30 = one-third (8 h)**.
There are no human answers yet. A form for humans to post answers is coming very soon!