Multiple choice

The radii of the bases of two cylinders are in the ratio $3 :5$ and their heights are in the ratio $2 : 3$. The ratio of their curved surface will be:

  1. $2 : 5$
  2. $2 : 3$
  3. $3 : 5$
  4. $5 : 3$
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A Correct answer
Explanation

Curved surface area of a cylinder = 2*pi*r*h. Ratio = (r1*h1) / (r2*h2) = (3*2) / (5*3) = 6/15 = 2/5.

AI explanation

The curved surface area of a cylinder is 2 times pi times r times h, meaning the ratio of the curved surface areas is the product of the ratios of their radii and heights. Multiply the radius ratio 3 : 5 by the height ratio 2 : 3 to get 3 times 2 : 5 times 3, which simplifies to 6 : 15. Reducing this by dividing both sides by 3 gives the final ratio of 2 : 5.