To calculate the volume of the life-sized sphere with a radius that is 44 inches longer than the model's radius of 6 inches, use the volume formula V = (4/3)πr³. The calculated volume is approximately 523,599 cubic inches when rounded to the nearest whole number.
To find the volume of the life-sized sphere, we first need to determine its radius. Since the diameter of the model is 12 inches, its radius is 6 inches. The life-sized sphere's radius is 44 inches longer than the model's, so the life-sized sphere's radius is 6 + 44 = 50 inches.
The formula for the volume of a sphere is V = (4/3)πr³. Plugging in the life-sized sphere's radius, we get the volume V = (4/3)π(50)³ cubic inches.
Calculating this volume, we have V = (4/3)π(125,000) ≈ 523,598.78 cubic inches. Rounding to the nearest whole number, the final answer is 523,599 cubic inches.
In conclusion, the volume of the life-sized sphere is approximately 523,599 cubic inches when rounded to the nearest whole number.