What is the piston displacement of a master cylinder with a 1.5-inch diameter bore and a 4-inch stroke?

What is the piston displacement of a master cylinder with a 1.5-inch diameter bore and a 4-inch stroke?

• A. 6.28 cubic inches
• B. 7.0686 cubic inches
• C. 8.25 cubic inches
• D. 5.5 cubic inches

Answer: (B)

To calculate the piston displacement of a master cylinder, you can use the formula for the volume of a cylinder, which is: \[ V = \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius of the cylinder, and \( h \) is the height (or stroke) of the cylinder. In this case, the bore diameter is given as 1.5 inches, so the radius is half of that: \[ r = \frac{1.5}{2} = 0.75 \text{ inches} \] The stroke (height) of the cylinder is given as 4 inches. Substituting these values into the formula: 1. First, calculate \( r^2 \): \[ r^2 = (0.75)^2 = 0.5625 \text{ square inches} \] 2. Then, multiply \( r^2 \) by the height (stroke): \[ V = \pi \times 0.5625 \times 4 \] 3. Now incorporating \( \pi \) (approximately 3.1416): \[ V \approx 3.1416 \times 0

To calculate the piston displacement of a master cylinder, you can use the formula for the volume of a cylinder, which is:

[ V = \pi r^2 h ]

where ( V ) is the volume, ( r ) is the radius of the cylinder, and ( h ) is the height (or stroke) of the cylinder. In this case, the bore diameter is given as 1.5 inches, so the radius is half of that:

[ r = \frac{1.5}{2} = 0.75 \text{ inches} ]

The stroke (height) of the cylinder is given as 4 inches. Substituting these values into the formula:

1. First, calculate ( r^2 ):

[

r^2 = (0.75)^2 = 0.5625 \text{ square inches}

]

2. Then, multiply ( r^2 ) by the height (stroke):

[

V = \pi \times 0.5625 \times 4

]

3. Now incorporating ( \pi ) (approximately 3.1416):

[

V \approx 3.1416 \times 0