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Two Steel Sheets Each of Length A1 And Breadth A2 Are Used to Prepare the Surfaces of Two Right Circular Cylinders ⇀ One Having Volume V1 And Height A2 And Other Having Volume V2 And Height A1. Then, - Mathematics

MCQ

Two steel sheets each of length a1 and breadth a2 are used to prepare the surfaces of two right circular cylinders ⇀ one having volume v1 and height a2 and other having volume v2 and height a1. Then, 

Options

  • v1 = v2

  • a1v1 = a2v2

  •  a2v1 = a1v2

  • \[\frac{v_1}{a_1} = \frac{v_2}{a_2}\]

     

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Solution

Let the radius of the base of the cylinders be r and R.
Now, let sheet with length a1 be used to form a cylinder with volume v1
So,

\[2\pi r = a_1 \]

\[ \Rightarrow r = \frac{a_1}{2\pi}\]

Volume

\[v_1 = \pi r^2 h = \pi \left( \frac{a_1}{2\pi} \right)^2 a_2 = \frac{{a_1}^2 a_2}{4\pi}\]

Similarly, let sheet with length a2 be used to form a cylinder with volume v2
So,

\[2\pi r = a_1 \]

\[ \Rightarrow r = \frac{a_1}{2\pi}\]

Volume 

\[v_2 = \pi R^2 h = \pi \left( \frac{a_2}{2\pi} \right)^2 a_1 = \frac{{a_2}^2 a_1}{4\pi}\]
Now,

\[\frac{v_1}{v_2} = \frac{{a_1}^2 a_2}{{a_2}^2 a_1} = \frac{a_1}{a_2}\]

\[ \Rightarrow v_1 a_2 = v_2 a_1\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Q 19 | Page 30
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