To determine the correct equation for finding the area of the circular lid (base) of the conical bird feeder, we need to recall the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
For this problem, we are given the volume [tex]\( V = 64.3 \)[/tex] cubic centimeters and the height [tex]\( h = 7 \)[/tex] centimeters. Simplifying the formula by recognizing that [tex]\( \pi r^2 \)[/tex] represents the area of the base [tex]\( B \)[/tex], we can rewrite the volume formula as:
[tex]\[ V = \frac{1}{3} B h \][/tex]
We want to solve this equation for [tex]\( B \)[/tex]. Let's substitute the given values for [tex]\( V \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ 64.3 = \frac{1}{3} B \cdot 7 \][/tex]
So, the equation we use to find the area of the circular lid (base) of the conical bird feeder is:
[tex]\[ 64.3 = \frac{1}{3} B \cdot 7 \][/tex]
Among the given options, this corresponds to:
[tex]\[ 64.3 = \frac{1}{3} (B) (7) \][/tex]
Thus, the correct equation to use is:
[tex]\[ 64.3 = \frac{1}{3} (B) (7) \][/tex]
