related rates

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.1

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.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?

• 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.6

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?

• 86π cm²/min

• 89π cm²/min

• 80π cm²/min

• 71π cm²/min

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.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?

• 1296π in³/sec

• 1294π in³/sec

• 1303π in³/sec

• 1305π in³/sec

Tags

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.6

CCSS.HSG.SRT.C.8