Here is a Post on Finding Volume of a Solid by shell Method set up and Evaluating the integral.
Topic : Volume of a Solid
On Integration also one can find out volume of any solid.
Question : Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis
y = 2x, y = 4, x = 0
Solution :
We know that the volume of the solid formed by rotating the area between the curves of f(x)
and g(x) and the lines x = a and x = b about the y-axis is given by
The graph of the line “ y = 2x” and “y = 4” between the two axes is denoted by the shaded region in the graph drawn below:
So, the volume of the shaded region when revolved around y-axis is given by:
Hence, the volume of the solid generated by revolving the curves “ y = 2x” and “y = 4” around y axis in the interval [0,2] is “16π /3”.
If you have any queries do write to our calculus help.
Topic : Volume of a Solid
On Integration also one can find out volume of any solid.
Question : Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis
y = 2x, y = 4, x = 0
Solution :
We know that the volume of the solid formed by rotating the area between the curves of f(x)
and g(x) and the lines x = a and x = b about the y-axis is given by
The graph of the line “ y = 2x” and “y = 4” between the two axes is denoted by the shaded region in the graph drawn below:
So, the volume of the shaded region when revolved around y-axis is given by:
Hence, the volume of the solid generated by revolving the curves “ y = 2x” and “y = 4” around y axis in the interval [0,2] is “16π /3”.
If you have any queries do write to our calculus help.
