A right rectangular prism with dimensions of 2 cm 5 cm and 10 cm is shown.
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Answer:
Step-by-step explanation:
If you plot the directrix and the focus, you can see that the focus is to the left of the directrix. Since a parabola ALWAYS wraps itself around the focus, our parabola opens sideways, to the left to be specific. The formula for the parabola that opens to the left is
We will solve this for x at the end. The negative is out front because it opens to the left. If it opened to the right, it would be positive.
The vertex of a parabola is exactly halfway between the focus and the directrix, so our vertex coordinates h and k are (3, 6). P is defined as the distance between the vertex and the directrix, or the vertex and the focus. Since the vertex is directly between both the directrix and the focus, each distance is the same. P = 1. Filling in what we have now:
which simplifies to
Now we will solve it for x.
and
so
Volume of a cylinder is defined as:
v = volume
r = radius
h = height.
V = (r^2)h
In this problem,
v = 1,356.48 in^3
r = 6 in
h = ?
Plug our numbers into the volume formula above.
1,356.48 in^3 = (6^2)h
Divide both sides by (6^2) to isolate variable h
12.0 = h
The height of the cylinder is 12.0 inches