Final answer:
The total volume of all six identical cylinders, each with a height of 6.5 inches and a radius of 2.4 inches, is calculated to be 705.705 cubic inches, indicating that all provided answer options are incorrect.
Step-by-step explanation:
To find the total volume of all six identical cylinders in an engine, we first need to calculate the volume of one cylinder using the formula for the volume of a cylinder:
V = πr²h
where:
- V is the volume of the cylinder,
- π (pi) is approximately 3.14159,
- r is the radius of the base of the cylinder,
- h is the height of the cylinder.
For one cylinder with a height (h) of 6.5 inches and a radius (r) of 2.4 inches, we substitute the values into the formula:
V = 3.14159 × (2.4 inches)² × 6.5 inches
After calculating, we get the volume of one cylinder and then multiply that value by 6 to get the total volume of all six cylinders.
Here's the step-by-step calculation:
- Calculate the base area (πr²):
3.14159 × (2.4 inches)² = 3.14159 × 5.76 inches² = 18.095 inches² - Multiply the base area by the height to find the volume of one cylinder:
18.095 inches² × 6.5 inches = 117.6175 cubic inches - Multiply the volume of one cylinder by the number of cylinders (6):
117.6175 cubic inches × 6 = 705.705 cubic inches
Therefore, the total volume of all six identical cylinders is 705.705 cubic inches, which makes all the provided answer options incorrect.