Question
A circular cardboard piece is needed for the base of a volcano model. The volcano is 46 centimeters tall and has a volume of 800 cubic centimeters. Which equation can be used to find the area of the circular base?
46 = one-third (B) squared (800)
46 = one-third (B) (800)
800 = one-third (B squared) (46)
800 = one-third (B) (46)
46 = one-third (B) squared (800)
46 = one-third (B) (800)
800 = one-third (B squared) (46)
800 = one-third (B) (46)
Answers
GPT-4o mini
To find the area of the circular base (B), we can use the formula for the volume of a cone:
\[
V = \frac{1}{3} B h
\]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
In your case, the volume \( V = 800 \) cubic centimeters and the height \( h = 46 \) centimeters.
Plugging these values into the formula gives:
\[
800 = \frac{1}{3} B (46)
\]
This matches with the equation you provided:
\[
800 = \frac{1}{3} (B) (46)
\]
Thus, this is the correct equation to use to find the area of the circular base \( B \).
\[
V = \frac{1}{3} B h
\]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
In your case, the volume \( V = 800 \) cubic centimeters and the height \( h = 46 \) centimeters.
Plugging these values into the formula gives:
\[
800 = \frac{1}{3} B (46)
\]
This matches with the equation you provided:
\[
800 = \frac{1}{3} (B) (46)
\]
Thus, this is the correct equation to use to find the area of the circular base \( B \).