| Direction: Study the following information carefully and answer the given questions. |
| Give answer |
| What is the volume of a cylinder? |
| I. The diameter of the cylinder is equal to the side of a square whose perimeter is 28 cm and its height is equal to that of the length of a rectangle whose perimeter is 154 cm. |
| II. The lateral surface area of a cylinder is 2112 \[c{{m}^{2}}\] and the circumference of the base is 88 cm. |
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 statements I and II together are not sufficient to answer the question.
E) if the data in both statements I and II together are necessary to answer the question.
Correct Answer: B
Solution :
From I. Perimeter of the square = 28 cm \[\therefore \] Side of the square = 7 cm So, diameter of the cylinder = 7 cm Radius of the cylinder = 3.5 cm Perimeter of the rectangle = 2(L + B) = 154 cm \[\therefore \] L + B = 77 cm As we don?t know any relation between length and breadth we can?t find the height of the cylinder. Form II. Surface area\[=2\pi RH=2112\] ?.(i) Circumference = \[2\pi R=88\] ?.(ii) Then, \[R=\frac{88\times 7}{2\times 22}=14\,cm\] \[\therefore \] Putting the value of R in (i), we get \[\therefore \] \[H=\frac{2112\times 7}{2\times 22\times 14}=24\,cm\] Volume \[=\pi {{R}^{2}}H=\frac{22}{7}\times 14\times 14\times 24\] \[=14784\,\,c{{m}^{3}}\] Hence II alone is sufficient to answer the question.
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