Related Rates

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec
• -7.2 ft/sec
• 7.2 ft/sec
• 12

Tags

CCSS.8.G.B.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

• 40pi in/sec

Tags

CCSS.7.G.B.4

All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing each edge is 1 centimeter.

• -12 cm^3/sec

• -9 cm^3/sec

• 12 cm^3/sec

• 9 cm^3/sec

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

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.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.8.G.C.9

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.8.G.B.8

Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm³/sec.  How fast is the diameter changing when the diameter is 8 cm?

• -1/(16pi) cm/sec
• -1/16 cm/sec
• -1/(4pi) cm/sec
• 1/(4pi) cm/sec

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.8.G.C.9

CCSS.HSG.GMD.A.3

Devin set up a toy rocket. For safety, he stands 6 meters from the rocket. He sets off the rocket and it heads straight up at a constant rate of 4 m/s.  How fast is the distance between the rocket and Devin changing after 2s?

• -2.5 m/s
• 2.5 m/s
• 3.2 m/s
• -3.2 m/s

Tags

CCSS.HSA.SSE.A.1

A baseball diamond is a square with a side of 90 ft. Tucker hits the ball and runs towards first base at 16 ft/sec.  How fast is the distance between second base and Tucker changing when he is 30 ft from first base?

• 8.875 ft/sec
• 5.060 ft/sec
• -5.060 ft/sec
• -8.875 ft/sec

Tags

CCSS.8.G.B.8