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A three-dimensional render of a smooth, shiny sphere. The sphere is set against a graded backdrop that transitions from light to dark, simulating a sense of depth. Layers of transparent concentric rings surround this sphere from the center, indicating the growth of the radius over time, but without any specific measurements or numbers. To the side of the sphere, five different arrows pointing towards it, each representing a potential radius size, but again, without any specific measurements or text.

1. The radius of a sphere is r inches at time t seconds. Find the radius when the rates of increase of the surface area and the radius are numerically equal.

A
1/4π in
B
1/5π in
C
1/3π in
D
1/8π in
E
1/2π in

a = 4πr^2

da/dt = 8πr dr/dt
if the rates are the same,
1 = 8πr, so r = 1/(8π)
So, (D)

thanks steve

thanks Steve

thanks Steve

thanks steve

thanks steve

thanks steve

Thanks Steve

thanks steve

Thanks, Steve.