What is the volume of a hemisphere with a radius of 34.1 in, rounded to the nearest tenth of a cubic inch?

To find the volume of a hemisphere, we can use the formula: \[ V = \frac{2}{3} \pi r^3 \] where: - \( V \) is the volume of the hemisphere, - \( r \) is the radius of the hemisphere. Given that the radius of the hemisphere is 34.1 inches, we can substitute this value into the formula to find the volume. Let's calculate the volume of the hemisphere with a radius of 34.1 inches. Calculate the value by following steps: - step0: Calculate: \(\frac{2}{3}\pi \times 34.1^{3}\) - step1: Convert the expressions: \(\frac{2}{3}\pi \left(\frac{341}{10}\right)^{3}\) - step2: Multiply: \(\frac{2\pi }{3}\left(\frac{341}{10}\right)^{3}\) - step3: Evaluate the power: \(\frac{2\pi }{3}\times \frac{341^{3}}{10^{3}}\) - step4: Rewrite the expression: \(\frac{2\pi }{3}\times \frac{341^{3}}{2^{3}\times 5^{3}}\) - step5: Reduce the numbers: \(\frac{\pi }{3}\times \frac{341^{3}}{2^{2}\times 5^{3}}\) - step6: Multiply the fractions: \(\frac{\pi \times 341^{3}}{3\times 500}\) - step7: Multiply: \(\frac{341^{3}\pi }{1500}\) The volume of the hemisphere with a radius of 34.1 inches is approximately 83046.579703 cubic inches. Rounded to the nearest tenth of a cubic inch, the volume of the hemisphere is approximately 83046.6 cubic inches.