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Here is problem 1:
A rocket is launched from a platform 10 feet from the ground. At its peak, it is 180 feet high and has traveled 100 feet from the base of the platform.
What would the equation be for that? The platform has the coordinates of (0,10)
Problem 2:
A cylinder is inscribed in a sphere, which has the radius 20. Call the height of the cylinder h and the radius of the cylinder r.
A) Make an equation in terms of r.
B) What is the maximum and minimum volumes it can have?
Hey Psyche.
A similar question has been asked before to this about inscribing a cylinder. Did you ask this question previously in this forum?
If not I can try and dig out the thread.
1. Use the form $\displaystyle y = a(x - h)^2 + k$ where $\displaystyle (h,k)$ is the vertex of the parabola.Quote:
Originally Posted by Psyche
2. Sketch a side view represented by a rectangle inscribed in a circle centered at the origin.
radius of cylinder, $\displaystyle r = x$
height of the cylinder, $\displaystyle h = 2y = 2\sqrt{20^2 - x^2}$
use the formula for the volume of a cylinder to get the volume in terms of x. To find the max and min, you could graph the volume function in your calculator, otherwise you'd need to use optimization techniques from calculus.
the largest rectangle inscribed in a circle is a square so I would assume that the largest volume cylinder would have a length of 40/rad2 and a radius of 20/rad2. Smallist is a cylinder infinitely thin
