Answer:
Step-by-step explanation:
What is the volume of the square prism?
Recall the formula for the volume of any prism can be represented by the equation
[tex]V=b*h[/tex], where V is the prism's volume, b is the area of the prism's base, and h is the height of the prism.
Since the base is a square, we can just multiply the side length of the base by itself to get the area (since the area of a square is just the side length squared):
8 * 8 = 64 = b
Now that we have that, we can plug in our values into the equation for volume:
V = b * h
V = (64) * (6)
V = 384
What is the volume of a cone?
Also, recall the formula for the volume of any cone can be represented by the equation
[tex]V= \frac{1}{3} \pi r^2h[/tex], where V is the cone's volume, r is the radius of the cone's base, and h is the height of the prism.
Note that because the cone is inscribed into the prism, it will have the following measurements
diameter = s = 8
height = h = 6
Since the equation requires a radius and not a diameter to be plugged in, we can divide the diameter by two to get the radius:
r = 8/2 = 4
Now that we have everything to plug into our equation, let's do just that:
[tex]V= \frac{1}{3} \pi r^2h[/tex]
V = 1/3 * (3.142) * (4)^2 * (6) [lets round pi to 3.142]
V = 101
What is the probability that the bee will land in the cone?
If we assume that it can only land in the prism, then the probability of the bee landing inside of the cone is simply the volume of the cone divided by the volume of the prism:
101/384
0.263
0.263 * 100%
26%
Therefore, the bee has a 26% chance of landing in the prism.
