this hydraulic lift is designed to lift a 3,000 - pound car. the diameter of the cylinder under the car at…

Explanation:

Step1: Convert diameter of Piston 1 to feet

1 inch = $\frac{1}{12}$ feet, so 6 inches = $6\times\frac{1}{12}=0.5$ feet.

Step2: Calculate area of Piston 1

The area formula for a circle is $A = \pi r^{2}$, where $r$ is the radius. For Piston 1, $r_1=\frac{d_1}{2}=\frac{0.5}{2}=0.25$ feet. Then $A_1=\pi r_1^{2}=3.14\times(0.25)^{2}=3.14\times0.0625 = 0.19625\approx0.2$ $ft^{2}$.

Step3: Calculate area of Piston 2

For Piston 2, $d_2 = 3$ feet, $r_2=\frac{d_2}{2}=\frac{3}{2}=1.5$ feet. Then $A_2=\pi r_2^{2}=3.14\times(1.5)^{2}=3.14\times2.25 = 7.065\approx7$ $ft^{2}$.

Answer:

$A_1 = 0.2$ $ft^{2}$; $A_2 = 7$ $ft^{2}$