Related Rates, Word Problems

A conical tank is being filled with water at a rate of 3 cubic meters per minute. If the tank has a height of 10 meters and a radius of 5 meters, how fast is the water level rising when the water is 6 meters deep?

• 1/25 m/min

• 1/30 m/min

• 1/20 m/min

• 1/35 m/min

A spherical balloon is being inflated at a rate of 4 cubic meters per minute. If the radius of the balloon is 2 meters, how fast is the radius increasing when the radius is 3 meters?

• 1/9 m/min

• 1/12 m/min

• 1/18 m/min

• 1/15 m/min

A cylindrical tank is being filled with water at a rate of 5 cubic meters per minute. If the tank has a height of 8 meters and a radius of 3 meters, how fast is the water level rising when the water is 4 meters deep?

• 5/18 m/min

• 5/21 m/min

• 5/24 m/min

• 5/27 m/min

A rectangular swimming pool is being filled with water at a rate of 6 cubic meters per minute. If the pool has a length of 10 meters, a width of 4 meters, and a depth of 2 meters, how fast is the water level rising when the water is 1 meter deep?

• 3/20 m/min

• 3/25 m/min

• 3/15 m/min

• 3/10 m/min

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

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