Dylan works out and burns 10 calories per minute swimming and 7 calories per minute biking. He wants to burn a minimum of 600 ca
lories. Due to daylight limitations, the time Dylan spends swimming must be no less than twice the time he spends biking.
1 answer:
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Due to the symmetry of the paraboloid about the <em>z</em>-axis, you can treat this is a surface of revolution. Consider the curve , with
, and revolve it about the <em>y</em>-axis. The area of the resulting surface is then
But perhaps you'd like the surface integral treatment. Parameterize the surface by
with and
, where the third component follows from
Take the normal vector to the surface to be
The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:
Then the area of the surface is
which reduces to the integral used in the surface-of-revolution setup.