Question

a cylinder measuring 5.7 cm wide and 6.9 cm high is filled with gas. the piston is pushed down with a steady force measured to be 25. n. calculate the pressure of the gas inside the cylinder. write your answer in units of kilopascals. be sure your answer has the correct number of significant digits. kpa

Explanation:

Step1: Calculate the radius of the cylinder

The width of the cylinder is its diameter \(d = 5.7\ cm\). The radius \(r=\frac{d}{2}=\frac{5.7}{2}\ cm = 2.85\ cm\). Convert radius to meters: \(r = 2.85\times10^{- 2}\ m\) (since \(1\ m=100\ cm\)).

Step2: Calculate the area of the piston

The area of a circle \(A=\pi r^{2}\). Substitute \(r = 2.85\times10^{-2}\ m\) into the formula: \(A=\pi\times(2.85\times 10^{-2})^{2}\ m^{2}\approx2.55\times10^{-3}\ m^{2}\).

Step3: Calculate the pressure

The formula for pressure \(P=\frac{F}{A}\). Given \(F = 25\ N\) and \(A\approx2.55\times10^{-3}\ m^{2}\). Then \(P=\frac{25}{2.55\times10^{-3}}\ Pa\approx9800\ Pa\). Convert to kilopascals: \(P=\frac{9800}{1000}\ kPa = 9.8\ kPa\) (rounded to two significant digits as \(25\) has two significant digits and \(5.7\) has two significant digits).

Answer:

\(9.8\ kPa\)