Hey there!
Good luck on your assignment and enjoy your day!
~
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.
All corresponding angles of similar triangle are equal.
Answer:
142 in^2
Step-by-step explanation:
Base: 7 × 3 = 21 (×2 = 42)
Small faces: 5 × 3 = 15 (×2 = 30)
Larger faces: 5 × 7 = 35 (×2 = 70)
Add: 21 + 30 + 70 = 142
Answer:
It depends on the person, I personally work better plugging in numbers and practicing with numbers I like. I say just try different ways and see what works best for you.