The radius of the sphere below is 6 centimeters (cm). What is the volume, in cubic centimeters, of the sphere?

Rationale

The volume of the sphere is 904.32 cubic centimeters.

To calculate the volume of a sphere, the formula \( V = \frac{4}{3} \pi r^3 \) is used, where \( r \) is the radius. Plugging in the radius of 6 cm into this formula yields a volume of approximately 904.32 cubic centimeters.

A (904.32) CORRECT

This choice is correct because when applying the formula for the volume of a sphere, \( V = \frac{4}{3} \pi (6)^3 \), we compute \( V \approx \frac{4}{3} \times 3.14 \times 216 \approx 904.32 \) cubic centimeters.

B (150.72) YOUR ANSWER

This volume is incorrect as it does not correspond to the calculation of a sphere's volume with a radius of 6 cm. If we evaluate \( \frac{4}{3} \pi (3.25)^3 \) or similar values, they yield volumes significantly lower than expected for a radius of 6 cm.

C (25.12) YOUR ANSWER

This value is also incorrect. It seems to reflect a miscalculation or confusion with a much smaller radius. The volume of a sphere with a radius of 6 cm cannot be as low as 25.12 cubic centimeters, since even a sphere with a radius of 1 cm has a volume greater than this.

D (75.36) YOUR ANSWER

This choice is mistaken as well. The volume of a sphere with a radius of 6 cm is vastly underestimated here. The calculation for a sphere of such size results in a much larger volume than 75.36 cubic centimeters, which might be a miscalculation for a smaller sphere radius.

Conclusion

The correct volume of a sphere with a radius of 6 cm is 904.32 cubic centimeters, derived from the standard volume formula. The other options reflect significant underestimations of the sphere's volume, emphasizing the importance of accurately applying the formula to determine three-dimensional space accurately.

The radius of the sphere below is 6 centimeters (cm). What is the volume, in cubic centimeters, of the sphere?

The volume of the sphere is 904.32 cubic centimeters.

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