Multiple choice

From a closed cardboard cylinder of height $30\;cm$ and diameter of base $21\;cm,\;15$ rectangles of size $2\;cm\times1.5\;cm$ are cut out. Find the total surface area of the remaining cylinder.

  1. $1628\;cm^2$
  2. $2528\;cm^2$
  3. $2618\;cm^2$
  4. $2628\;cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total surface area of cylinder = 2*pi*r*(r+h). Diameter = 21, so r = 10.5. Area = 2 * (22/7) * 10.5 * (10.5 + 30) = 66 * 40.5 = 2673. Area of 15 rectangles = 15 * (2 * 1.5) = 45. Remaining area = 2673 - 45 = 2628.

AI explanation

The total surface area of the closed cylinder is 2*pi*r*(h+r) = 2 * (22/7) * 10.5 * (30 + 10.5) = 66 * 40.5 = 2673 square cm. The total area of the 15 cut-out rectangles is 15 * (2 * 1.5) = 45 square cm. Thus, the surface area of the remaining cylinder is 2673 - 45 = 2628 square cm.

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