GATE 2017 EC – Question 37
A three dimensional region R of finite volume is described by $x^2 + y^2 \leq z^3$; $0 \leq z \leq 1$, where $x, y, z$ are real. The volume of R (up to two decimal places) is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.78 to 0.79
Explanation
At height $z$ the cross-section is a disc with $r^2 = z^3$, so its area is $\pi z^3$. The volume is $\int_0^1 \pi z^3\,dz = \frac{\pi}{4} = 0.785$.