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) 2(B) 16.5(C) 8(D) 13.5
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) 2(B) 16.5(C) 8(D) 13.5
Volume Formula: The formula for the volume of a cube is V=s3, where s is the length of a side.
Rate of Change: To find the rate of change of the volume, we need to differentiate the volume with respect to time, so dtdV=3s2⋅dtds.
Given Values: Given dtds (rate of change of the side) is 2km/h, and s (side length) is 1.5km.
Plug in Values: Plug the values into the formula: dtdV=3×(1.5km)2×(2km/h).
Calculate Rate: Calculate the rate of change of the volume: dtdV=3×2.25km2×2km/h.
Simplify Calculation: Simplify the calculation: dtdV=3×4.5km3/h×2.
Finish Calculation: Finish the calculation: dtdV=27km3/h.
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