Question

Hey guys! I would be thankful if anyone could help me answer this question.
A can manufacturing company needs to purchase labels for the cans they produce. They are planning to produce 200,000 cans that will have a height of 20cm and a radius of 5 cm. If the labels cover the entire curved surface of each can, how many square metres of material will be required to label all the cans?

Answer 1

In order to not get confused, start by converting cm to m
h=20 cm = 0.2m and r=5cm = 0.05m

The cans are cylinders and we only need the rectangular shape, which is equal to the height x the circumference of the circle (2r(pi)), which you'll have to multiply by 200,000 for the number of cans necessary

your equation is therefore:
A=200,000h(2pi(r))
A=200,000(0.2)(2)(0.05)(pi)
A=4000pi m^2

Answer 2

Surface area for a cylinder = 2πrh

r = 5cm, h= 20cm

Surface area for one can =  2πrh = 2*π*5*20 = 200π = 200* 3.14

Surface area ≈ 628 cm²

For the 200, 000 cans, Total area = 200 000 * 628 = 125 600 000 cm²

But 1 000 000 cm² = 1m²

125 600 000 cm² =     125 600 000 / 1 000 000 = 125.6 m²

Total surface area ≈ 125.6 m²