Question
Zula has a conical bird feeder with a volume of 64.3 cubic centimeters and a height of 7 centimeters. Which equation can be used to find the area of the circular lid needed to cover the bird feeder?
64.3 = one-third (7) (h)
64.3 = one-third (B) (7)
64.3 = one-third (B squared) (7)
64.3 = one-third (B) (7) squared
64.3 = one-third (7) (h)
64.3 = one-third (B) (7)
64.3 = one-third (B squared) (7)
64.3 = one-third (B) (7) squared
Answers
GPT-4o mini
To find the area of the circular lid needed to cover the conical bird feeder, we first need to note that the formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base of the cone, and \( h \) is the height.
Given that the volume \( V \) of the bird feeder is 64.3 cubic centimeters and the height \( h \) is 7 centimeters, we can rewrite the formula for our specific case:
\[ 64.3 = \frac{1}{3} \pi r^2 (7) \]
Now, rearranging this equation will yield the area of the circular lid (the base area of the cone), which is determined by \( B = \pi r^2 \).
So, to express this in terms of the area \( B \):
\[ 64.3 = \frac{1}{3} B (7) \]
This simplifies to:
\[ B = \frac{3 \times 64.3}{7} \]
This derived equation uses \( B \) (the area of the circular lid) and involves calculating based on the volume and height.
Therefore, the correct equation that represents the relationship to find the area of the circular lid is:
**64.3 = one-third (B)(7)**.
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base of the cone, and \( h \) is the height.
Given that the volume \( V \) of the bird feeder is 64.3 cubic centimeters and the height \( h \) is 7 centimeters, we can rewrite the formula for our specific case:
\[ 64.3 = \frac{1}{3} \pi r^2 (7) \]
Now, rearranging this equation will yield the area of the circular lid (the base area of the cone), which is determined by \( B = \pi r^2 \).
So, to express this in terms of the area \( B \):
\[ 64.3 = \frac{1}{3} B (7) \]
This simplifies to:
\[ B = \frac{3 \times 64.3}{7} \]
This derived equation uses \( B \) (the area of the circular lid) and involves calculating based on the volume and height.
Therefore, the correct equation that represents the relationship to find the area of the circular lid is:
**64.3 = one-third (B)(7)**.