Answer:
Hemisphere Circumference: 31.95
The volume of a hemisphere is \frac{\pi }{324}
cubic mile. Find the circumference of the base of the hemisphere.
The volume of a hemisphere is given by the formula:
V = (2/3)πr³
where r is the radius of the hemisphere.
Since we are given the volume of the hemisphere as π/324 cubic miles, we can solve for the radius:
π/324 = (2/3)πr³
r³ = (1/2)(324/π)
r³ = 162/π
r = (162/π)^(1/3)
Now, the circumference of the base of the hemisphere is given by:
C = 2πr
Substituting the value of r, we get:
C = 2π(162/π)^(1/3)
C ≈ 31.95 miles (rounded to two decimal places)
Therefore, the circumference of the base of the hemisphere is approximately 31.95 miles