Related Rates Questions (Please show all steps) 5. If a spherical snowball melts
ID: 2852058 • Letter: R
Question
Related Rates Questions (Please show all steps)
5. If a spherical snowball melts so that its surface area decreases at a constant rate of 1 cm2 /min, find the rate at which the diameter is changing when the diameter is 6 cm.
6. You are blowing a bubble out of chewing gum. The gum in the bubble can be modeled as the space between two concentric spheres. As the bubble expands, the volume of the gum making up the bubble remains constant, so the thickness of the bubble decreases. After 15 seconds of bubble-blowing, the inner radius of the bubble is 6 cm, while the thickness of the bubble is 0.1 cm. At that time, the inner radius of the bubble is increasing at 2 cm/sec; at what rate is the thickness of the bubble decreasing?
7. Big Ben is the nickname of London’s famous clock tower. The hour hand of Big Ben is 9 feet long, while the minute hand is 14 feet long. Consider the distance between the tip of the minute hand and the tip of the hour hand. How is this distance changing when Big Ben shows 2:20
Explanation / Answer
5) surface area of sphere S = 4r2 = 4 (d/2)2
==> S = d2
differentiating with respect to t
==> dS/dt = (2d) dd/dt
given that dS/dt = 1cm2/min , d = 6cm
==> 1 = (2(6)) dd/dt
==> dd/dt = 0.02653
Hence diameter is decreasing at a rate of 0.02653 cm/min