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

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

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.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.HSG.GMD.A.1

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 = -36 cm²/hr
• dV/dt = -36 cm³/hr
• dA/dt = 120 cm²/hr
• dS/dt = 10 cm²/hr

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the height of the water changing when the water is 2 ft deep?

• -9/(8pi) ft/sec
• 9/(8pi) ft/sec
• -8/(9pi) ft/sec
• 8/(9pi) f/tsec

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.MG.A.1

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

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.HSG.GMD.A.1

CCSS.HSA.SSE.A.1

Rain is falling into a cylindrical barrel at the rate of 20 cm³ per minute. If the radius of the base is 18 cm, how fast is the water rising?

• .2 cm/sec
• 1.11 cm/sec
• .9 cm/sec
• .02 cm/sec

A boat is being pulled into dock by means of a winch 12 feet above the deck of the boat. The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 13 feet of rope out.

• h=tanθ
• r=cos(12)
• ax²+bx+c=0
• a²+b²=c²

Tags

CCSS.8.G.B.8