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31.03.2020 •
Mathematics
(4) A spherical balloon is being inflated so that its diameter is increasing at a constant rate of 6 cm/min. How quickly is the volume of the balloon increasing when the diameter is 50 cm
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Ответ:
In terms of its radius
, the volume of the balloon is
The diameter
is twice the radius, so that in terms of its diameters, the balloon's volume is given by
Differentiate both sides with respect to time
:
The diameter increases at a rate of
. When the diameter is
, we have
or about 23,562 cc/min (where cc = cubic centimeters)
Ответ: