) the length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3cm/s. when the length is
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So we have three points A(4,3), B(4,4) and C(7,4).
We introduce a fourth point D(7,3).
We obtain a rectangle ABCD. By rotating the rectangle,
around the y axis, we get two cylinders. Denote the
first cylinder C1 and the inner cylinder with vertices AB by C2.
Computing the volume of C1:
Computing the volume of the cylinder C2:
In order to find the volume of the <span>hollow tube, simply compute the difference of the two obtained values like this:
</span>
Now, in order to find the <span>volume of the solid generated by revolving the region enclosed by the triangle, simply divide the previous </span>value over two like this:
Answer
We introduce a fourth point D(7,3).
We obtain a rectangle ABCD. By rotating the rectangle,
around the y axis, we get two cylinders. Denote the
first cylinder C1 and the inner cylinder with vertices AB by C2.
Computing the volume of C1:
Computing the volume of the cylinder C2:
In order to find the volume of the <span>hollow tube, simply compute the difference of the two obtained values like this:
</span>
Now, in order to find the <span>volume of the solid generated by revolving the region enclosed by the triangle, simply divide the previous </span>value over two like this:
Answer