Rotation In Maths I

Calculus Level 5

There is a Figure bounded by the graphs of

1) $y^{2} = 4x$

2) $y=0$

3) $x=0$

4) $x=1$

It is Rotated About the Line $x=1$ .

Then The Volume of the Resulting Solid Figure Can Be Expressed As

$\dfrac{a\pi}{b}$ .

Then Find $\textbf {a + b}$ .

This Problem Is A Part Of Rotation In Maths .

The answer is 31.

1 solution

Arghyadeep Chatterjee
Jan 16, 2019

For volume of revolution about any line by disc method we use the formula dV = $\pi$ (SP)^2 d(AS) Where AS is the line about which the curve is rotated and SP is the perpendicular from a particular point P on the curve . Now in order to find out d(AS) we generally use the Pythagorean Theorem and then differentiate to find the differential element d(AS) in terms of dx or dy or a suitable parameter. But in this case AS is simply dy as the line x=1 is parallel to Y-axis . So the volume would be such that SP is the perpendicular distance from point P from the line x =1 . So the volume is

Which is $\pi$ $\frac{16}{15}$

Rotation In Maths I

The answer is 31.

1 solution

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