What is the diameter of a hemisphere with a volume of 5990, in, cubed, comma5990 in

3
, to the nearest tenth of an inch?

3 answers

To find the diameter of a hemisphere with a given volume, we can use the formula for the volume of a hemisphere:

V = (2/3) * pi * r^3

Where V is the volume and r is the radius of the hemisphere. Since we're looking for the diameter, we need to find the radius first.

Given that the volume is 5990 in^3, we can set up the equation:

5990 = (2/3) * pi * r^3

Solving for r, we find:

r = (3 * 5990 / (2 * pi)) ^ (1/3)
r ≈ 12.7 inches

The diameter of the hemisphere is twice the radius, so:

D = 2 * r
D ≈ 25.4 inches

Therefore, the diameter of the hemisphere with a volume of 5990 in^3 is approximately 25.4 inches.
are you sure
Let's double-check the calculations:

Given:
V = 5990 in^3

Using the formula for the volume of a hemisphere:
V = (2/3) * pi * r^3

Substitute the given volume:
5990 = (2/3) * pi * r^3

Solve for r:
r^3 = (5990 * 3) / (2 * pi)
r^3 = 8985 / (2 * pi)
r^3 ≈ 1430.88
r ≈ 11.3 inches

The diameter of the hemisphere is twice the radius:
D = 2r
D ≈ 22.6 inches

Therefore, to the nearest tenth of an inch, the diameter of a hemisphere with a volume of 5990 in^3 is approximately 22.6 inches.