<p>A ballon in the shape of a cylinder has hemispherical ends of the same radius as that of a cylinder. The ballon is being inflated at the rate of 261pi cubic centimeters per minute. At the instant the radius of the cylinder is 3 centimeters, the volume of the ballon is 144pi cubic centimeters and the radius of the cylinder is increasing at the rate of 2 centimeters per minute. (The volume of a cylinder with radius r and height h is (pi<em>r^2</em>h) The volume of a sphere with radius r is (4<em>pi</em>(r^3) / 3) .</p>
<p>A) At this instant, what is the height of the cylinder?</p>
<p>B) At this instant, how fast is the height of the cylinder increasing?</p>
<p>Your solutions to this tough problem will be very much appreciated. thank you for your help.</p>