In an automobile engine, the bore of a cylinder is its diameter, and the stroke of a cylinder is the height swept by the piston. Find the swept volume of a cylinder with a bore of 367 In. and a stroke of 4.50 in.

To find the swept volume of a cylinder, we can use the formula for the volume of a cylinder: \[ V = \pi r^2 h \] where: - \( V \) is the volume of the cylinder, - \( r \) is the radius of the cylinder (which is half of the bore), - \( h \) is the height of the cylinder (which is the stroke). Given: - Bore of the cylinder = 367 in. - Stroke of the cylinder = 4.50 in. First, we need to find the radius of the cylinder by dividing the bore by 2. \[ r = \frac{367}{2} \] Next, we can substitute the values of the radius and the stroke into the formula for the volume of a cylinder to find the swept volume. Calculate the value by following steps: - step0: Calculate: \(\pi \left(\frac{367}{2}\right)^{2}\times 4.5\) - step1: Multiply the numbers: \(\frac{367^{2}}{2^{2}}\times \pi \times 4.5\) - step2: Multiply the terms: \(\frac{367^{2}\pi }{2^{2}}\times 4.5\) - step3: Convert the expressions: \(\frac{367^{2}\pi }{2^{2}}\times \frac{9}{2}\) - step4: Multiply the numbers: \(\frac{1101^{2}\pi }{2^{3}}\) - step5: Reorder the terms: \(\frac{\pi \times 1101^{2}}{2^{3}}\) - step6: Evaluate the power: \(\frac{\pi \times 1101^{2}}{8}\) - step7: Expand the expression: \(\frac{1101^{2}\pi }{8}\) The swept volume of the cylinder with a bore of 367 in. and a stroke of 4.50 in. is approximately 476,030.22 cubic inches.