a) The amount of metal used to make the can is 351.9 cm²
b) The amount of paper used to make the label is 251.1 cm².
How to calculate surface area cylinder.
The amount of metal used to make the can is same as the total surface area of the can.
a) Total surface area = area of the two circular bases + area of the curved surface
Area of circuit = πr²
For the two circles = 2πr²
Area of curved surface = 2πrh
where
r is radius
h is height
Given that
r = d/2 = 8/2 = 4 cm
h = 10 cm
TSA = 2πr² + 2πrh
= 2πr(r +h)
Substitute
TSA = 2*3.142*4(4+10)
= 25.136(14) = 351.9 cm²
The amount of metal used to make the can is 351.9 cm²
b) Material for label = area of the curve surface
Curved surface area = 2πrh
CSA = 2 * 3.142 * 4 * 10
= 251.1 cm²
The amount of paper used to make the label is 251.1 cm²