all the edges of a cube are expanding at a rate of 8 inches per second. how fast

Question

all the edges of a cube are expanding at a rate of 8 inches per second. how fast is the surface area changing in square inches per second when each edge is 1 inches? do not include units in your answer. all the edges of a cube are expanding at a rate of 8 inches per second. how fast is the surface area changing in square inches per second when each edge is 1 inches? do not include units in your answer. all the edges of a cube are expanding at a rate of 8 inches per second. how fast is the surface area changing in square inches per second when each edge is 1 inches? do not include units in your answer.

Explanation / Answer

surface area of cube S=6 x^2

where edge length =x =1

differentiate with respect to t

dS/dt=12 x dx/dt (dx/dt =8 since edges are increasing at 8 inch pr sec)

=12*1*8

=96

surface area is increasing at 96 square inches per second

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