Find the volume of a cone with a radius of 4 in and a height of 6 in.

Rationale

100.48 in cubed.

The volume of a cone is calculated using the formula \( V = \frac{1}{3} \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Substituting the given values (radius = 4 in, height = 6 in), we find that the volume is approximately 100.48 in³.

A (66.65 in cubed) YOUR ANSWER

This value does not accurately represent the volume of the cone. Using the formula, substituting the values for the radius and height, results in a larger volume than this option suggests. It likely results from miscalculating the cone volume or using an incorrect formula.

B (150.72 in cubed) YOUR ANSWER

This option overestimates the volume of the cone. The calculation of the cone's volume yields a result less than this figure, indicating that a mistake was made in either applying the formula or inputting the radius and height values.

C (301.44 in cubed) YOUR ANSWER

This choice significantly exceeds the actual volume of the cone. The calculation should yield a number much lower than this, indicating an error in calculations, such as misapplying the volume formula or incorrect arithmetic.

D (100.48 in cubed) CORRECT

This is the correct volume of the cone, calculated using the formula \( V = \frac{1}{3} \pi (4)^2 (6) \). Performing the computations gives approximately 100.48 in³, confirming its accuracy.

Conclusion

The volume of a cone is determined by its radius and height through a specific formula that accounts for its geometric properties. In this case, the values provided lead to a calculated volume of 100.48 in³, making option D the only correct choice. The other options stem from miscalculations, highlighting the importance of applying the correct formula and careful arithmetic in geometric volume problems.

Find the volume of a cone with a radius of 4 in and a height of 6 in.

100.48 in cubed.

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