CAN SOMEONE HELP ME IN THIS INTEGRAL QUESTION PLS ''Find the surface area between the z = 1 and z = 4 planes of z = x ^ 2 + y ^ 2 paraboloid.''

Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve , with , and revolve it about the y-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.

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

sorry can't

step-by-step explanation:

i googled though and something came up but it was in science langueage not common english sooo