Multiple choice

If the curved surface area of a solid right circular cylinder of height $h$ and radius $r$ is one-third of its total surface area, then

  1. $\displaystyle h\, =\, \frac{1}{3}\, r$
  2. $\displaystyle h\, =\, \frac{1}{2}\, r$
  3. $h = r$
  4. $h = 2r$
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B Correct answer
Explanation

Curved surface area (CSA) = 2*pi*r*h. Total surface area (TSA) = 2*pi*r*h + 2*pi*r^2. Given CSA = 1/3 * TSA. 2*pi*r*h = 1/3 * (2*pi*r*h + 2*pi*r^2). 6*pi*r*h = 2*pi*r*h + 2*pi*r^2. 4*pi*r*h = 2*pi*r^2. 2h = r, so h = r/2.

AI explanation

The curved surface area formula is 2 times pi times r times h, and the total surface area formula is 2 times pi times r times (r plus h). Setting the curved surface area equal to one third of the total surface area gives 2 times pi times r times h equals two thirds times pi times r times (r plus h). Dividing both sides by 2 times pi times r leaves h equals one third times (r plus h), which simplifies to 3h equals r plus h, resulting in h equals one half times r.

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