Question 30

The approximate volume of a sphere with a diameter of 8 in is 266 in cubed.

The volume of a sphere can be calculated using the formula \( V = \frac{4}{3} \pi r^3 \). Given a diameter of 8 inches, the radius is 4 inches. Substituting this value into the formula yields a volume of approximately 268.08 in cubed, which rounds to 266 in cubed.

A) 266 in cubed

This option is correct as it accurately reflects the calculated volume of the sphere based on the given diameter. After applying the formula for the volume of a sphere using a radius of 4 inches, the computation aligns with this choice.

B) 290.96 in cubed

This option is incorrect as it does not match the calculated volume of the sphere. The value of 290.96 in cubed likely results from an error in calculation or misunderstanding of the volume formula, as it exceeds the correct volume.

C) 201 in cubed

This option is also incorrect. The volume of 201 in cubed is significantly less than the correct volume derived from the radius of 4 inches. It indicates a misunderstanding of the calculations required for determining sphere volume.

D) 300 in cubed

This option is incorrect as it overestimates the volume of the sphere. The calculation shows that the actual volume is much lower than 300 in cubed, indicating a failure to apply the volume formula correctly.

Conclusion

The correct answer is 266 in cubed, as determined through the proper application of the volume formula for a sphere. All other options fail to represent the accurate volume due to either miscalculations or incorrect interpretations of the sphere's dimensions. Thus, option A remains the only valid choice based on the mathematical derivation.