13. Determine the length of BD, given by x in the figure. Give your answer to two decimal places.
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We know that the volume of a sphere of radius r is given by
Now, we have been given the initial volume was 4,188.79 cubic centimeters. Let us find the radius at this time.
Substituting the value of volume in the above equation, we get
Now, the final volume is given by 14,137.167 cubic centimeters. Thus, we have
Now, let us find the surface areas for these two radii.
For
Surface area is given by
Similarly, for
Therefore, the increase in the surface area is given by
Hence, the average rate at which the surface area is changing is given by
Therefore, the average rate at which the surface area is changing is given by 130.8 square centimeters per second.