Question

The net of a cylinder is shown below.

a) Work out the length x, in mm.
b) What is the total surface area of the cylinder, in
mm²?
Give your answers in terms of .
5 mm
5 mm
I
[4 mm

Answer 1

a) Using Pythagoras' theorem, we can find the length x:

x² = 5² + 4²
x² = 25 + 16
x² = 41
x = sqrt(41) mm

b) The total surface area of the cylinder is the sum of the areas of the two circles and the rectangle:

Total surface area = 2πr² + 2πrh
Total surface area = 2π(4 mm)² + 2π(4 mm)(5 mm)
Total surface area = 32π + 40π
Total surface area = 72π mm²

Therefore, the total surface area of the cylinder is 72π mm².