If r = 8 units and x = 8 units, then what is the total surface area of the cylinder shown above?
1 answer:
The surface area of a cylinder is the area of the top and bottom circle and the side of the cylinder, which is really a rectangle with the circumference of the circle for the length and x for the width.
So the formula is
Plug in r and x into the equation;
which is about 804.25 square units since it is an area.
Hope this helps.
So the formula is
Plug in r and x into the equation;
which is about 804.25 square units since it is an area.
Hope this helps.
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Let . The tangent plane to the surface at (0, 0, 8) is
The gradient is
so the tangent plane's equation is
The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation
or ,
, and
.
(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
