# A piston, A, has a diameter of 0.53 cm. A second piston, B, has a diameter of 3.5 cm. Determine the force, F, necessary to support the 500.0 N weight in the absence of friction. The key relationship is that the Pressure at piston A (Pa) equals the pressure at piston B (Pb).  Pa = Pb

Pressure equals force divided by area.  P = F/A

So you have:  Fa/Aa = Fb/Ab

The area of a circle is pi r^2.

The force on piston B is...

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The key relationship is that the Pressure at piston A (Pa) equals the pressure at piston B (Pb).  Pa = Pb

Pressure equals force divided by area.  P = F/A

So you have:  Fa/Aa = Fb/Ab

The area of a circle is pi r^2.

The force on piston B is 500 N and the radius is 1.75 cm.

The force on piston A is unknown, and the radius is 0.275 cm

Substituting into the equation:

Fa/(pi* .275^2) = 500 /( pi*1.75^2)

Solve for Fa = .275^2/1.75^2 * 500

Fa = 12.35 N

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