A hypothetical cube grows so that the length of its sides are increasing at a rate of 4 m/min. How fast is the volume of the cube increasing when the sides are 7 m each? Calculus Applications of Derivatives Using Implicit Differentiation to Solve Related Rates Problems 1 Answer Eddie Aug 16, 2016 #= 588 \ m^3 "/min"# Explanation: #V = l^3# #(dV)/dt =3 l^2 (dl)/dt# #= 3 (7)^2* 4 = 588 \ m^3 "/min"# Answer link Related questions If a cylindrical tank with radius 5 meters is being filled with water at a rate of 3 cubic... If the radius of a sphere is increasing at a rate of 4 cm per second, how fast is the volume... If #y=x^3+2x# and #dx/dt=5#, how do you find #dy/dt# when #x=2# ? If #x^2+y^2=25# and #dy/dt=6#, how do you find #dx/dt# when #y=4# ? How do you find the rate at which water is pumped into an inverted conical tank that has a... How much salt is in the tank after t minutes, if a tank contains 1000 liters of brine with 15kg... At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the... At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the... What is the rate of change of the width (in ft/sec) when the height is 10 feet, if the height is... What is the total amount of water supplied per hour inside of a circle of radius 8 if a... See all questions in Using Implicit Differentiation to Solve Related Rates Problems Impact of this question 11303 views around the world You can reuse this answer Creative Commons License