Nets Math Example 4

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Example 4

hard
A cylindrical can has radius 33 cm and height 1010 cm. Describe its net and find the total surface area.

Solution

  1. 1
    Step 1: The net of a cylinder consists of two circles (top and bottom lids) and one rectangle (the lateral surface unrolled).
  2. 2
    Step 2: The rectangle's width equals the height of the cylinder (1010 cm), and its length equals the circumference of the circle (2πr=6π2\pi r = 6\pi cm).
  3. 3
    Step 3: Area of two circles: 2πr2=2π(9)=18π2\pi r^2 = 2\pi(9) = 18\pi cm².
  4. 4
    Step 4: Area of rectangle: 6π×10=60π6\pi \times 10 = 60\pi cm². Total SA=18π+60π=78π≈245.0SA = 18\pi + 60\pi = 78\pi \approx 245.0 cm².

Answer

SA=78π≈245.0SA = 78\pi \approx 245.0 cm²
The cylinder's net is two circles plus one rectangle. The rectangle's longer dimension is the circumference 2π(3)=6π2\pi(3) = 6\pi and its shorter dimension is the height 10. Summing: 2π(3)2+2π(3)(10)=18π+60π=78π2\pi(3)^2 + 2\pi(3)(10) = 18\pi + 60\pi = 78\pi cm².

About Nets

A net is a two-dimensional layout of all the faces of a three-dimensional solid, arranged so that folding along the edges produces the original solid. Nets reveal the surface area as the sum of flat face areas.

Learn more about Nets →

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