The side of a cube is increasing at a rate of 2 kilometers per hour.At a certain instant, the side is 1.5 kilometers.What is the rate of change of the volume of the cube at that instant (in cubic kilometers per hour)?Choose 1 answer:(A) 13.5(B) 16.5(C) 8(D) 2
Q. The side of a cube is increasing at a rate of 2 kilometers per hour.At a certain instant, the side is 1.5 kilometers.What is the rate of change of the volume of the cube at that instant (in cubic kilometers per hour)?Choose 1 answer:(A) 13.5(B) 16.5(C) 8(D) 2
Volume Formula: Volume of a cube formula: V=s3, where s is the side length.
Differentiate Volume: Differentiate the volume with respect to time to find the rate of change of volume: dtdV=3s2⋅dtds.
Plug in Values: Plug in the values: s=1.5km and dtds=2km/h.dtdV=3×(1.5)2×2.
Calculate Rate: Calculate the rate of change: dtdV=3×2.25×2.
Simplify Calculation: Simplify the calculation: dtdV=3×4.5×2.
Final Calculation: Final calculation: dtdV=13.5×2.
More problems from Calculate unit rates with fractions