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###### Vijay posted an Question
January 11, 2022 • 20:08 pm 30 points
• IIT JAM
• Physics (PH)

# In these type of questions, how to draw the figure for visualization? how to solve this 0problem using cartesian cordinates?

Considera region bounded by the surfaces x and 5. The volume ofregion is, O 25 T O 25 T O 25 T 4 O 50 Here. +y - p-p= The volume of the region is. - =5 d pdpdodz - 27 =0 =0p=0 =0

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• ##### Isha lohan 1 Best Answer

First of all to visualise this type of questions you need to first visualise it in 2D image, like, you put the Z equal to zero then you see that it is a circles equation, it means that if there is no z-axis it will make a circle on the x-y plane. And if you try to put x is equals to zero or Y is equals to zero, any one of them, then you will see that it is something like a parabola type of equation. Now, combine both things, a parabola from base with a circle at top. By these simple considerations, you can try to visualise graphs, although they may not be very precise. Secondly to find volume in 3D Cartesian coordinate, you may do triple integration wrt dx dy dz, with proper limits. But that will make calculation lengthy and complicated, therefore we mostly prefer spherical coordinate if our figure is given in any curve shape. For any curved shape, prefer spherical or cylindrical coordinate rather than Cartesian.

ask if any doubt.

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