Find the approximate volume of a sphere with a diameter of 8 in.
The approximate volume of a sphere with a diameter of 8 in is 266 in cubed.
To find the volume of a sphere, we use the formula \( V = \frac{4}{3} \pi r^3 \). With a diameter of 8 inches, the radius is 4 inches. Plugging this into the formula gives us an approximate volume of 268.08 in³, which rounds to 266 in³ when considering significant figures.
This choice closely approximates the calculated volume of the sphere. Using the formula \( V = \frac{4}{3} \pi (4)^3 \) results in approximately 268.08 in³, which rounds to 266 in³. This makes it the most accurate answer based on the given diameter.
This volume does not correctly reflect the radius derived from the diameter of 8 inches. If the radius were larger than 4 inches, this answer might be plausible, but calculations indicate that the volume is actually lower due to the smaller radius. Thus, this choice overestimates the volume.
This volume is significantly lower than the actual calculated volume. It suggests a radius that is too small or miscalculates the volume entirely. The formula applied to a radius of 4 inches yields a much higher figure due to the cubic relationship in the volume calculation.
This option also overestimates the volume of the sphere. The volume calculated with a radius of 4 inches does not support this choice, and it fails to adhere to the geometric principles governing the volume of a sphere.
In summary, the correct volume of a sphere with an 8-inch diameter, calculated using the appropriate formula, is approximately 266 in³. This makes choice A the correct answer, while the other options either overestimate or underestimate the actual volume based on the geometric properties of a sphere. Understanding the calculation process is essential for accurately determining the volume based on given dimensions.
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