<1> the length of a rectangle is 4 inch more than its width and the 4 inch diffe

Question

<1> the length of a rectangle is 4 inch more than its width and the 4 inch difference is maintained as the rectangle increases its size. find the instantaneous rate of change of the are of the rectangle with respect to its width w when w=3in. <2> a spherical balloon is being inflated so that its volume is increasing at the rate of 5 in^3/min. find the rate at which the diameter is increasing when the diameter is 12inch. <3> sand is being poured at the rate of 10 m^3/min onto a conical pile. if the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 8m high?

please show complete solutions with answer. dont cite sites.

Explanation / Answer

1. A = w*(w+4)

dA/dw = 2w + 4

at w= 3

dA/dw = 10

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