| Directions: These questions consist of a question and two statements I and II given below them. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and choose the appropriate option, [LIC (AO) 2014] |
| What is the volume of the cylinder (in\[{{m}^{3}}\])? |
| I. The sum of height and radius of the cylinder is 24 m. The surface area of the cylinder is \[2112\,{{m}^{2}}.\] |
| II. LCM and HCF of the numerical values of the radius and height of the cylinder are 70 and 2, respectively. The square of numerical values of the radius of the cylinder is 96 more than the square of the numerical value of the height of the cylinder. |
A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C) If the data either in statement I alone or in statement II alone are sufficient to answer the question.
D) If the data in both the statements I and II together are not sufficient to answer the question
E) If the data in both the statements I and II together are necessary to answer the question.
Correct Answer: E
Solution :
| According to the statement I, |
| \[H+R=24\,m\] ... (i) |
| and \[2\pi RH=2112\,{{m}^{2}}\] |
| According to the statement II, |
| \[RH=70\times 2=140\,m\] |
| \[\Rightarrow \] \[{{R}^{2}}-{{H}^{2}}=96\] |
| \[\Rightarrow \] \[(R+H)(R-H)=96\] |
| \[\Rightarrow \] \[24\,(R-H)=96\] |
| \[R-H=4\,m\] ... (ii) |
| On solving Eqs. (I) and (ii), we get |
| \[\Rightarrow \] \[R=14\,m\] |
| \[H=10\,m\] |
| \[\therefore \] Volume of cylinder\[=\frac{22}{7}\times 14\times 14\times 10\] |
| \[=22\times 2\times 140\] |
| \[=22\times 280=6160\,{{m}^{3}}\] |
| \[\therefore \] Both statements are necessary to furnish the answer. |
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