22) what is the constant of proportionality?\ntime (h) wages (w)\n3 $27.00\n5 $45.00\n6 $54.00\n23) find the…

22) what is the constant of proportionality?\ntime (h) wages (w)\n3 $27.00\n5 $45.00\n6 $54.00\n23) find the area of the cross section if the diameter of the cylinder is 6 inches and the height is 10 inches.

22) what is the constant of proportionality?\ntime (h) wages (w)\n3 $27.00\n5 $45.00\n6 $54.00\n23) find the area of the cross section if the diameter of the cylinder is 6 inches and the height is 10 inches.

Answer

Explanation:

Step1: Calculate constant of proportionality

The formula for the constant of proportionality $k$ in a proportional relationship $w = kh$ (where $w$ is wages and $h$ is time) is $k=\frac{w}{h}$. For the first row, $k=\frac{27}{3}=9$. We can check with other rows: for the second row $\frac{45}{5} = 9$, for the third row $\frac{54}{6}=9$.

Step2: Calculate cross - section area

The cross - section of a cylinder is a circle. The formula for the area of a circle is $A=\pi r^{2}$, where $r$ is the radius. Given the diameter $d = 6$ inches, the radius $r=\frac{d}{2}=\frac{6}{2}=3$ inches. Then $A=\pi\times3^{2}=9\pi\approx9\times3.14 = 28.26$ square inches.

Answer:

  1. The constant of proportionality is 9.
  2. The area of the cross - section is 28.26 square inches.