## Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides

Question

Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 3 in. long and increasing at the rate of 0.2 in./s. How fast is the volume of the cube changing (in cu in/s) at that instant of time?

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Math
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2021-10-01T06:15:32+00:00
2021-10-01T06:15:32+00:00 1 Answer
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## Answers ( )

Answer:DV(t) = 5.4 in³/sStep-by-step explanation:Volume of cube of side x is Vc = x³If the sides are increasing at a rate 0.2 in/sec and sides of a cube are 3 in.V(t) = x³Taking derivatives on both sides of the equation we getDV(t) = 3*x² * dx/dt (2)Plugging values in equation (2)DV(t) = 3* (3)²* 0,2 ⇒ DV(t) = 5.4 in³/s