To find the correct equation to calculate the area of the circular base [tex]\( B \)[/tex] of the given volcano model, we need to apply the formula for the volume of a cone. The volume [tex]\( V \)[/tex] of a cone is given by the formula:
[tex]\[ V = \frac{1}{3} B h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( B \)[/tex] is the area of the base,
- [tex]\( h \)[/tex] is the height.
Here, we have:
- Volume [tex]\( V = 800 \)[/tex] cubic centimeters,
- Height [tex]\( h = 46 \)[/tex] centimeters.
Our goal is to match this information to one of the given equations.
### Step-by-Step Solution:
1. Start by writing the formula for the volume of the cone:
[tex]\[ V = \frac{1}{3} B h \][/tex]
2. Substitute the given values [tex]\( V = 800 \)[/tex] and [tex]\( h = 46 \)[/tex] into the formula:
[tex]\[ 800 = \frac{1}{3} B \cdot 46 \][/tex]
3. Rearrange the equation to isolate [tex]\( B \)[/tex]:
[tex]\[ B = \frac{3 \cdot 800}{46} \][/tex]
Thus, the equation that correctly represents this relationship is:
[tex]\[
800 = \frac{1}{3} B \cdot 46
\][/tex]
### Comparison with Given Options:
After examining the provided options, we find:
- [tex]\( 46 = \frac{1}{3}(B)^2(800) \)[/tex]
- [tex]\( 46 = \frac{1}{3}(B)(800) \)[/tex]
- [tex]\( 800 = \frac{1}{3}(B^2)(46) \)[/tex]
- [tex]\( 800 = \frac{1}{3}(B)(46) \)[/tex]
The correct choice matches exactly with our derived equation:
[tex]\[
800 = \frac{1}{3}(B)(46)
\][/tex]
So, the equation that can be used to find the area of the circular base [tex]\( B \)[/tex] of the cone is:
[tex]\[ 800 = \frac{1}{3}(B)(46) \][/tex]
