Multiple choice

Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: Find the height of the cylinder. I. The Curved surface area of the cylinder is 396 cm2 and the total surface area of the cylinder is 1628 cm2.II. The radius of the cylinder is 0.5 cm more than the 3 times of the height of the cylinder.

  1. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in statements I alone or in statement II alone is sufficient to answer the question.

  4. The data in both the statements I and II is not sufficient to answer the question.

  5. The data in both the statements I and II together is necessary to answer the question.
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A Correct answer
Explanation

Curved Surface Area (CSA) = 2*pi*r*h = 396. Total Surface Area (TSA) = 2*pi*r*h + 2*pi*r^2 = 1628. TSA - CSA = 2*pi*r^2 = 1628 - 396 = 1232. From this, r can be found, and subsequently h. Statement I is sufficient. Statement II provides a relation between r and h, but without another independent equation, it is not sufficient.

AI explanation

Using the cylinder surface area formulas, statement I provides two equations: curved surface area is 2*pi*r*h = 396 and total surface area is 2*pi*r*(r+h) = 1628. Dividing the total surface area by the curved surface area eliminates h, giving (r+h)/h = 1628/396, which simplifies to 1 + r/h = 4.11. This allows us to solve for the ratio of r to h, and substituting it back into the first equation yields a definite height. Statement II gives r = 3h + 0.5, which is a single equation with two variables and cannot find the height alone. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

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