document.write( "Question 1208484: Find the volume of the solid generated by rotating the region enclosed by the curve 𝑦^2 = 16𝑥, the 𝑥 axis and the ordinate 𝑥 = 4 about:
\n" ); document.write( "a) The 𝑥 axis
\n" ); document.write( "b) The 𝑦 axis
\n" ); document.write( "c) The line 𝑥 = 4
\n" ); document.write( "d) The line 𝑥 = 8
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Algebra.Com's Answer #847021 by Shin123(626) $\"\"$ $\"About$

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We use the Washer Method for all of these.
\n" ); document.write( "a)
\n" ); document.write( "Note that we only consider the part above the x-axis. (the region below the x-axis gives the same results). This means that $\"y=4%5Csqrt%28x%29\"$ . This gives the volume as

.
\n" ); document.write( "b)
\n" ); document.write( "We integrate with respect to $\"y\"$ this time, since we're rotating about the y-axis. Note that at $\"x=4\"$ , $\"y=8\"$ . (again, we're only considering the part above the x-axis) The outer radius is always $\"4\"$ , and the inner radius for a given $\"y\"$ is the corresponding x-value, which is $\"y%5E2%2F16\"$ . This means that the volume is

.
\n" ); document.write( "c)
\n" ); document.write( "We also integrate with respect to $\"y\"$ . For a given $\"y\"$ , the radius is $\"4-x\"$ (no outer/inner radius this time), or $\"4-y%5E2%2F16\"$ . This means the volume is

.
\n" ); document.write( "d)
\n" ); document.write( "We integrate with respect to $\"y\"$ . The inner radius is $\"4\"$ , and the outer radius for a given $\"y\"$ is $\"8-x\"$ , or $\"8-y%5E2%2F16\"$ . This means the volume is

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