GATE 2020 EC – Question 61
For the solid $S$ shown below, the value of $\iiint_Sx\,dx\,dy\,dz$ (rounded off to two decimal places) is ________.
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Show answer and explanation
Correct answer: 2.24 to 2.26
Explanation
The solid is a triangular prism whose cross-section in the $y$-$z$ plane is a right triangle with legs 1 and 1 (area $\frac12$) and whose length runs along $x$ from 0 to 3. So the integral is $\int_0^3x\,dx\times\frac12=\frac{9}{2}\times\frac12=2.25$.