Related Rates Review

A block of ice in the shape of a cube originally having volume 1000 cm³ is melting in such a way that the length of each of its edges is decreasing at the rate of 1 cm/hr. At what rate is its surface area decreasing at the time its volume is 27 cm³?   Assume that the block of ice maintains its cubical shape.

• dA/dt = -120 cm²/hr
• dV/dt = -120 cm³/hr
• dA/dt = 10 cm²/hr
• dS/dt = 10 cm²/hr

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.2

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.B.6

A tank is in the form of an inverted cone having an altitude of 10 ft and a radius of 5 feet. Water is flowing into the tank at the rate of 1 ft³/min. How fast is the water level rising when the water is 3 ft deep?

• 3.4 ft/min
• .14 ft/min
• 1 ft/min
• 1/2  ft/min

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?

• -262π in³/sec

• -247π in³/sec

• -256π in³/sec

• -263π in³/sec

Tags

CCSS.HSG.GMD.A.3

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?

• 4/3 ft/sec

• 8/7 ft/sec

• 1 ft/sec

• 8/3 ft/sec

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

An observer stands 2400 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 200 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 700 ft from the ground?

• 56 ft/sec

• 57 ft/sec

• 52 ft/sec

• 61 ft/sec

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8