Determine the surface area of a label that covers the lateral surface of a cylindrical can with height 40 mm and diameter 24 mm.
area = 2πrh
sub in your values
I came up with 3014.4mm is this correct
close
why don't you use the π value of your calculator?
I got 3015.93
To determine the surface area of the label that covers the lateral surface of a cylindrical can, we need to calculate the lateral surface area of the can itself.
The lateral surface area of a cylindrical can is given by the formula:
Lateral Surface Area = 2πrh
Where r is the radius of the base of the can and h is the height of the can. In this case, since the diameter is given as 24 mm, we can find the radius (r) by dividing the diameter by 2:
r = diameter / 2 = 24 mm / 2 = 12 mm
Now we can calculate the lateral surface area:
Lateral Surface Area = 2πrh = 2π(12 mm)(40 mm)
To find the surface area of the label, we need to subtract the area covered by the top and bottom bases of the can. The area of each base is given by:
Base Area = πr^2
Since we have two bases, the total area covered by the bases is:
Total Base Area = 2πr^2 = 2π(12 mm)^2
Now we can calculate the surface area of the label:
Surface Area of Label = Lateral Surface Area - Total Base Area
Substituting the values we calculated earlier:
Surface Area of Label = 2π(12 mm)(40 mm) - 2π(12 mm)^2
Now, we can simplify and calculate the value:
Surface Area of Label = 960π mm^2 - 288π mm^2
Surface Area of Label = 672π mm^2 (approximately)
Therefore, the surface area of the label that covers the lateral surface of the cylindrical can is approximately 672π square millimeters.