Final answer:
To calculate the diameter of a sphere with a given volume, first find the radius using the volume formula, and then double the radius to get the diameter. The diameter for a sphere with a volume of 397 cubic meters is approximately 9.0 meters to the nearest tenth.
Step-by-step explanation:
To find the diameter of a sphere with a known volume, we use the formula for the volume of a sphere:
V = \frac{4}{3}\pi r^3
Where V is the volume and r is the radius of the sphere.
We can rearrange the formula to solve for the radius, and then double it to find the diameter:
r = \left(\frac{3V}{4\pi}\right)^{1/3}
D = 2r
Given the volume V is 397 cubic meters:
r = \left(\frac{3\times397}{4\pi}\right)^{1/3} meters
After calculating r, we double it to find the diameter:
D \approx 2 \times 4.52 \approx 9.0 meters (rounded to the nearest tenth)
The diameter of the sphere is approximately 9.0 meters to the nearest tenth.