calculate the weight of the piece of steel shown in the drawing. (this steel weighs 0.283 lb/in.³) the…

Explanation:

Step1: Calculate radius of base

The diameter of the base is $2.35$ inches, so the radius $r=\frac{2.35}{2}=1.175$ inches.

Step2: Calculate volume of cylinder

The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Here, $h = 4.5$ inches. So $V_{cylinder}=\pi\times(1.175)^{2}\times4.5\approx\pi\times1.380625\times4.5\approx19.57$ in³.

Step3: Calculate volume of cone

The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Here, $h = 1.5$ inches. So $V_{cone}=\frac{1}{3}\pi\times(1.175)^{2}\times1.5=\pi\times1.380625\times0.5\approx2.17$ in³.

Step4: Calculate total volume

$V = V_{cylinder}+V_{cone}\approx19.57 + 2.17=21.74$ in³.

Step5: Calculate weight

The weight $W$ is given by the density times the volume. The density is $0.283$ lb/in³. So $W=0.283\times21.74\approx6.2$ lb.

Answer:

$6.2$