Multiple choice

The ratio of the total surface area to the lateral surface area of the cylinder is $5 : 3$. Find the height of the cylinder, if the radius of the cylinder is $12 cm$.

  1. $18 cm$
  2. $16 cm$
  3. $20 cm$
  4. $14 cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total Surface Area (TSA) = 2 * pi * r * (r + h). Lateral Surface Area (LSA) = 2 * pi * r * h. Ratio TSA/LSA = (r + h) / h = 5/3. (12 + h) / h = 5/3. 36 + 3h = 5h, so 2h = 36, h = 18.

AI explanation

Using the total surface area formula 2 times pi times r times h plus 2 times pi times r squared and the lateral surface area formula 2 times pi times r times h, their ratio simplifies to h plus r divided by h equals 5 divided by 3. Substitute the radius 12 into the simplified ratio to get h plus 12 divided by h equals 5 divided by 3, which yields 3h plus 36 equals 5h. Solving this gives h equals 18 cm.

Keep practicing — related questions