Each of the questions below consists of a question and two statements numbered I and II are 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 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.
Give answer 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.
Give answer c: if the data in Statement I alone or in Statement II alone are sufficient to answer the question.
Give answer d: if the data in both the Statements I and II together are not sufficient to answer the question.
Give answer e: if the data in both the Statements I and II together are necessary to answer the question.
What is the volume of the cylinder (in cubic metre)?
(I) The sum of height and radius of the cylinder is 24m. The total surface area of the cylinder is 2112 sq. m.
(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.
Let radius = $$r$$ and height = $$h$$
Statement I : $$r + h = 24$$
=> Total surface area = $$2 \pi r (r + h) = 2112$$
=> $$2 \times \frac{22}{7} \times r \times 24 = 2112$$
=> $$r = \frac{2112 \times 7}{22 \times 48} = 14$$ m
=> $$h = 24 - 14 = 10$$ m
Since, both radius and height are known, we can find the volume of cylinder, $$V = \pi r^2 h$$
Statement I alone is sufficient.
Statement II : We know that, $$a \times b = L.C.M. (a,b) \times H.C.F. (a,b)$$
=> $$r h = 70 \times 2 = 140$$
and $$r^2 - h^2 = 96$$
Solving the above equations, we get $$r = 14$$ m and $$h = 10$$ m
We can find the volume of the cylinder.
Statement II alone is sufficient.
Thus, either statement alone is sufficient to answer the question.
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