solid metal support poles in the form of right cylinders are made out of metal with a density of 4.5 g/cm³…
solid metal support poles in the form of right cylinders are made out of metal with a density of 4.5 g/cm³. this metal can be purchased for $0.69 per kilogram. calculate the cost of a utility pole with a radius of 10.9 cm and a height of 790 cm. round your answer to the nearest cent. (note: the diagram is not drawn to scale)
Answer
Explanation:
Step1: Calculate the volume of the cylinder
The volume formula for a cylinder is $V = \pi r^{2}h$. Given $r = 10.9$ cm and $h=790$ cm. $V=\pi\times(10.9)^{2}\times790=\pi\times118.81\times790 = 93859.9\pi\ cm^{3}\approx93859.9\times 3.14 = 294710.086\ cm^{3}$
Step2: Calculate the mass of the metal
Use the density - mass - volume relationship $\rho=\frac{m}{V}$, where $\rho = 4.5\ g/cm^{3}$. So $m=\rho V$. $m = 4.5\times294710.086=1326195.387\ g$ Convert grams to kilograms: $m = 1326195.387\div1000 = 1326.195387\ kg$
Step3: Calculate the cost
The cost per kilogram is $$0.69$. So the total cost $C=0.69\times m$. $C = 0.69\times1326.195387=$915.074817\approx$915.07$
Answer:
$$915.07$