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

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

• A. 5.0686 cubic inches
• B. 6.0686 cubic inches
• C. 7.0686 cubic inches
• D. 8.0686 cubic inches

Answer: (C)

To determine the piston displacement of a master cylinder, you can use the formula for the volume of a cylinder, which is: \[ \text{Volume} = \pi \times r^2 \times h \] where: - \( \pi \) is approximately 3.1416, - \( r \) is the radius of the cylinder, - \( h \) is the height or stroke of the cylinder. In this case, the diameter of the master cylinder is 1.5 inches, so the radius \( r \) would be half of that: \[ r = \frac{1.5 \text{ inches}}{2} = 0.75 \text{ inches} \] The stroke \( h \) is given as 4 inches. Now, substituting the values into the formula: 1. Calculate \( r^2 \): \[ r^2 = 0.75^2 = 0.5625 \text{ square inches} \] 2. Now plug \( r^2 \) and \( h \) back into the volume formula: \[ \text{Volume} = \pi \times 0.5625 \text{ square inches} \

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

[ \text{Volume} = \pi \times r^2 \times h ]

where:

• ( \pi ) is approximately 3.1416,

• ( r ) is the radius of the cylinder,

• ( h ) is the height or stroke of the cylinder.

In this case, the diameter of the master cylinder is 1.5 inches, so the radius ( r ) would be half of that:

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

The stroke ( h ) is given as 4 inches. Now, substituting the values into the formula:

1. Calculate ( r^2 ):

[ r^2 = 0.75^2 = 0.5625 \text{ square inches} ]

2. Now plug ( r^2 ) and ( h ) back into the volume formula:

[ \text{Volume} = \pi \times 0.5625 \text{ square inches} \