| Directions: In each of the given questions, one question and two statements numbered I and II are given. You have to decide whether the data given in both the statements are sufficient to answer the question or not. Read both the statements and give answer. |
| What is the volume of the cylinder? (in\[{{m}^{3}}\]) |
| I. The radius of the cylinder is 21 m. |
| II. The sum of the height and radius of the cylinder is 29 m. The curved surface area of the cylinder is \[1056\,\,{{m}^{2}}.\] |
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 or in statement II alone are sufficient to answer the question
D) If the data in both the statements together are not sufficient to answer the question
E) If the data in both the statements I and II together are sufficient to answer the question
Correct Answer: B
Solution :
| From statement I, r = 21 m |
| From statement II, |
| \[r+h=29\] . (i) |
| \[2\pi rh=1056\] |
| \[\Rightarrow \] \[rh=\frac{1056\times 7}{2\times 22}=168\] |
| \[\therefore \] \[{{(r-h)}^{2}}={{(r+h)}^{2}}-4rh={{(29)}^{2}}-4\times 168\] |
| \[=841-672=169\] |
| \[\Rightarrow \] \[r-h=13\] . (ii) |
| On solving Eqs. (i) and (ii), we get |
| r = 21, +h = 8 |
| \[\therefore \] Volume \[=\pi {{r}^{2}}h=\frac{22}{7}\times 21\times 21\times 8=11088\,{{m}^{3}}\] |
| \[\therefore \] Only statement II is sufficient to find the volume of the cylinder. |
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