Find the volume of a right circular cone that has a height of 11.4 in and a base with a radius of 5.1 in . Round your answer to the nearest tenth of a cubic inch. Answer Attempt 1 out of 2 Submit Answer

To find the volume of a right circular cone, we can use the formula: \[ V = \frac{1}{3} \pi r^2 h \] where: - \( V \) is the volume of the cone, - \( r \) is the radius of the base of the cone, - \( h \) is the height of the cone. Given: - Height of the cone, \( h = 11.4 \) inches, - Radius of the base of the cone, \( r = 5.1 \) inches. Substitute the given values into the formula: \[ V = \frac{1}{3} \pi (5.1)^2 (11.4) \] Now, we can calculate the volume of the cone. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{3}\pi \times 5.1^{2}\times 11.4\) - step1: Convert the expressions: \(\frac{1}{3}\pi \left(\frac{51}{10}\right)^{2}\times 11.4\) - step2: Multiply the terms: \(\frac{19}{5}\pi \left(\frac{51}{10}\right)^{2}\) - step3: Multiply: \(\frac{19\pi }{5}\left(\frac{51}{10}\right)^{2}\) - step4: Evaluate the power: \(\frac{19\pi }{5}\times \frac{51^{2}}{10^{2}}\) - step5: Multiply the fractions: \(\frac{19\pi \times 51^{2}}{5\times 10^{2}}\) - step6: Multiply: \(\frac{49419\pi }{500}\) The volume of the right circular cone is approximately 310.508735 cubic inches. Rounding to the nearest tenth of a cubic inch, the volume of the cone is approximately 310.5 cubic inches.