Multiple choice

Directions: Select the correct alternative from the given choices. The ratio of the curved surface areas of two cylinders A and B is 2 : 3. If the ratio of the volumes of A and B is 4 : 5, find the ratio of the heights of A and B.

  1. 2/3

  2. 5/9

  3. 1/3

  4. 2/5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved surface area S = 2*pi*r*h and volume V = pi*r^2*h. The ratio of areas is (r1*h1) / (r2*h2) = 2/3. The ratio of volumes is (r1^2*h1) / (r2^2*h2) = 4/5. Dividing the volume ratio by the area ratio gives (r1/r2) = (4/5) / (2/3) = 6/5. Substituting r1/r2 into the area ratio: (6/5) * (h1/h2) = 2/3, so h1/h2 = (2/3) * (5/6) = 10/18 = 5/9.

AI explanation

The curved surface area of a cylinder is 2*pi*r*h, so (r1*h1) divided by (r2*h2) equals 2/3. The volume is pi*r squared*h, meaning (r1 squared*h1) divided by (r2 squared*h2) equals 4/5. Squaring the surface area ratio gives (r1 squared*h1 squared) divided by (r2 squared*h2 squared) equals 4/9. Dividing this squared area ratio by the volume ratio, (4/9) divided by (4/5), yields the height ratio (h1 divided by h2) as 5/9.

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