Multiple choice

Find the percentage increase in the total surface area when five cylinders of equal height are made from a solid cylinder of radius 3 cm and height 5 cm by cutting along the four planes parallel to the base.

  1. 134%

  2. 150%

  3. 240%

  4. 643%

  5. 86%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The original surface area is 2*pi*r^2 + 2*pi*r*h = 2*pi*9 + 2*pi*3*5 = 18*pi + 30*pi = 48*pi. Cutting the cylinder into 5 pieces creates 4 new cuts, each adding 2 circular faces of area pi*r^2 = 9*pi. Total added area is 8 * 9*pi = 72*pi. Percentage increase = (72*pi / 48*pi) * 100 = 1.5 * 100 = 150%.

AI explanation

The original total surface area of the solid cylinder is 2 times pi times 3 times 5 plus 3 squared, which equals 48 pi. Cutting the cylinder into five pieces along four parallel planes creates ten new circular faces, adding a total surface area of 10 times pi times 3 squared, which is 90 pi. The percentage increase is the new area minus the old area divided by the old area times 100, so 90 pi minus 48 pi divided by 48 pi times 100 equals 150 percent. The percentage increase in the total surface area is 150 percent.

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