Related Rates Practice

A certain medical procedure requires that a balloon be inserted into the stomach and then inflated. Model the shape of the balloon by a sphere of radius r. If r is increasing at the rate of 0.3 cm/min, how fast is the volume changing when the radius is 4 cm?

• 15.08 cm³/min
• 268.08 cm³/min
• 60.32 cm³/min
• 6.03 cm³/min

A ladder 13 feet long rests against a vertical wall and is sliding down the wall at the rate of 3 ft/s at the instant the foot of the ladder is 5 feet from the base of the wall. At this instant, how fast is the foot of the ladder moving away from the wall?

• dz/dt = 36/5 ft/sec
• dx/dt = 36/5 ft/sec
• dy/dt = 36/5 ft/sec
• dx/dt = 36/5 ft²/sec

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec.  How fast is the area of the outer circle changing when the diameter is 8 in?

• 80pi in/sec
• 20pi in/sec
• 60pi in/sec
• 4opi in/sec

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.1

(3 min) The area of a circular region is increasing at a rate of 96 π square meters per second. When the area of the region is 64 π square meters, how fast, in meters per second, is the radius of the region increasing?

• 6
• 8
• 16
• 4√3

Tags

CCSS.7.G.B.4

Hospital officials estimate that approximately N(p) = p² + 5p + 900 people will seek treatment in the emergency room each year if the population of the community is p thousand. The population is currently 20,000 and is growing at the rate of 1,200 per year. At what rate is the number of people seeking emergency room treatment increasing?

• 48 million people per year
• 21,200 people per year
• 3000 people per year
• 54 people per year