Related Rates Pools of Questions

The radius r of a sphere is increasing at a rate of 2 inches per minute.

Find the rate of change of the volume when r=6 inches.

Use V=(4/3)πr³ and leave your answer in terms of π

• dv/dt=656π in³/min

• dv/dt=144π in³/min

• dv/dt=288π in³/min

• dv/dt=48π in³/min

Tags

CCSS.HSG.GMD.A.3

All edges of a cube (sides) are expanding at a rate of 4 centimeters per second.  How fast is the volume changing if each edge is 2 centimeter?

Use V=s³

• dv/dt = 36 cm³/sec

• dv/dt = 96 cm³/sec

• dv/dt = 8 cm³/sec

• dv/dt = 48 cm³/sec

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

In a cone, find the rate of change of the volume if dr/dt is 2 inches per minute and the height is 3r when the radius is 6.

• S=πr√(r^2+h^2)
• V=πr²h
• V=(πr²h)/3
• V=(4/3)πr³

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.GMD.A.1

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?

Use A=πr² and leave your answer in terms of π

• 50π m²/min

• 47π m²/min

• 25π m²/min

• 10π m²/min

Tags

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

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?

Use V=(4/3)πr³ and leave your answer in terms of π

• -262π in³/sec

• -247π in³/sec

• -256π in³/sec

• -263π in³/sec

Tags

CCSS.HSA.SSE.A.1

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?

(Hint: Pythagorean Theorem: x² + y² = z²)

• -4/3 ft/sec

• -8/7 ft/sec

• -1 ft/sec

• -8/3 ft/sec

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.SRT.C.8

Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 10 cm?

Use A=πr² and leave your answer in terms of π

• 86π cm²/min

• 89π cm²/min

• 80π cm²/min

• 71π cm²/min

Tags

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

A spherical snowball is rolled in fresh snow, causing it to grow so that its radius increases at a rate of 4 in/sec. How fast is the volume of the snowball increasing when the radius is 9 in?

Use V=(4/3)πr³ and leave your answer in terms of π

• 1296π in³/sec

• 1294π in³/sec

• 1303π in³/sec

• 1305π in³/sec

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

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.8

CCSS.HSG.SRT.C.6

The edge of a sugar cube is increasing at the rate of 10 cm/sec. At what rate is the volume of the sugar changing when the edge is 4 inches?

(Use the formula  V=S³ )

• 480 cm³/sec

• 240 cm³/sec

• 640 cm³/sec

• 40 cm³/sec

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

CCSS.HSA.CED.A.2