Answer :
The volume of the sphere with an area of the great circle equal to 98.5m² is approximately 244.7 cubic meters.
To find the volume of a sphere, we need to know the radius or the area of the great circle. In this case, we are given the area of the great circle, which is 98.5m².
The formula to find the volume of a sphere is V = (4/3)πr^3, where V represents the volume and r is the radius of the sphere.
To find the radius, we need to determine the radius of the great circle. The radius of the great circle is equal to the radius of the sphere.
The formula for the area of a circle is A = πr^2, where A represents the area and r is the radius.
We are given the area of the great circle as 98.5m². Using the formula, we can solve for the radius of the great circle:
98.5 = πr^2
Solving for r, we get r ≈ √(98.5/π) ≈ 5.6 meters.
Substituting the radius value into the volume formula, we have:
V = (4/3)π(5.6)^3 ≈ 244.7 cubic meters.
Therefore, the volume of the sphere with an area of the great circle equal to 98.5m² is approximately 244.7 cubic meters when rounded to the nearest tenth.
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