Question

1. A hydraulic cylinder is used to raise the bucket on a front-end loader. The outputpiston measures 2 inches in diameter. Apressure of 1,800 pounds per square inch(psi) is applied to the piston.a. Find the area of the output piston to thenearest tenth.b. Find the force exerted by the piston usingthe correct number of significant digits.

Answer 1

To find the area of the piston, use the given diameter to find the radius and then replace in the formula of the area of a circle:

`A=\pi\cdot r^2`

Remember that radius is half the diameter, which means the radius is 1 inch in this case:

`\begin{gathered} A=\pi\cdot1^2 \\ A=\pi\text{ } \end{gathered}`

The area of the circle is pi, rounded to the nearest tenth, it is 3.1 square inches.

To find the force exerted by the piston, use the pressure in pounds per square inch as a rate or a conversion factor.

`3.1in\cdot(1800pounds)/(1in)=5580pounds`

The force exerted is 5580 pounds.