GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 32 of 65

Marks: +1, -0

A parabola

x=y^{2}

with

0 ≤ x ≤ 1

is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by

360^{∘}

around the

x

-axis is

Solution:

Volume of the solid of rotation obtained by rotating the shaded area by 360o around the x-axis is given by
volume

(V)=∫↙{0}↖{1} π y^{2} d x

Or,

V=∫↙{0}↖{1} π x d x=π(\;{x^{2}}/{2})_{0}^{1}=\;{π}/{2}

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