Respuesta :
Answer:
[tex]Volume = 2.40 inch^3[/tex]
Step-by-step explanation:
Given data:
inner radius of can 1.5 inch
height of can 9 inch
thickness of can dr = 0.02 inch
top and bottom thickness 0.05 inch
so dh = 0.05+ 0.05 = 0.10 inch
we know that
[tex]volume =\pi r^2 h[/tex]
By using total differentiation method we have
[tex]dV = \frac{\partial V}{\partial r} dr + \frac{\partial V}{\partial h} dh[/tex]
[tex]= \frac{\partial (\pi r^2 h) }{\partial r} dr + \frac{\partial (\pi r^2 h)}{\partial h} dh[/tex]
[tex] =\pi h\frac{\partial (r^2)}{\partial r} dr + \pi r^2\frac{\partial h}{\partial h} dh[/tex]
[tex]= \pi h(2r) dr + \pi r^2 dh[/tex]
puttinfg all value to get required value of volume
[tex]dV = = \pi h(2r) dr + \pi r^2 dh[/tex]
[tex]= \pi (9)(2\times 1.5)(0.02)+ \pi (1.5)^2 (0.10)[/tex]
[tex]Volume = 2.40 inch^3[/tex]
Volume of walls can be taken as outer - inner volume. The volume of the metal in the walls and top and bottom of the can is 2.41 inch³
How to find the volume of a container?
Take the volume of whole container(including walls), then subtract inner volume from it.
Volume of walls of container = Volume of container with walls' volume - inner volume of the container.
Thus, for the given case, as shown in the image attached, we get:
Total volume of metal used = volume of walls of can+ volume of top and bottom of the can
- Volume of walls of can = volume of can - volume of inner can
- Volume of can = [tex]\pi r^2 h = \pi (1.5 + 0.02)^2 \times 9 \approx 65.325 \: \rm inch^3[/tex]radius of total can = inner radius + thickness of wall)
- Volume of inner can = [tex]\pi r^2 h = \pi (1.5 )^2 \times 9 \approx 63.62 \: \rm inch^3[/tex]
Volume of walls of can = 65.325 - 63.62 ≈ 1.705 inch³
Volume of top and bottom are same. They're like very tiny heighted cylinder with same radius r = 1.5 inches (they aren't 1.5 + 0.02 since they've to fit in)
Thus,
Volume of top + bottom = 2 times volume of top = [tex]2 \times \pi (1.5)^2 \times 0.05 \approx 0.707 \: \rm inch^3[/tex]
Total volume of metal used ≈ 1.705 + 0.707 ≈ 2.41 inch³
Thus, The volume of the metal in the walls and top and bottom of the can is 2.41 inch³
Learn more about volume of cylinder here:
https://brainly.com/question/12763699
