Final answer:
The diameter of a hemisphere with a volume of 60570 cm³ is approximately 50.0 cm when calculated using the volume formula for a sphere and doubling the result to find the diameter.
Step-by-step explanation:
The student asks what is the diameter of a hemisphere with a volume of 60570 cm³ to the nearest tenth of a centimeter. To find the diameter, we first need to recognize that the volume of a hemisphere is half of the volume of a full sphere. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.
Since we have the volume for the hemisphere, we can set the equation for the volume of a sphere equal to twice the given volume because a hemisphere is half a sphere: 2 × 60570 cm³ = (4/3)πr³. Solving for r, we find the radius and then double it to find the diameter.
When we calculate it out, rounding to the nearest tenth of a centimeter, we find that the diameter of the hemisphere with a volume of 60570 cm³ is approximately 50.0 cm.