The radius of the base of a right circular cone is increasing at the rate of \( 3 \mathrm{~cm} \...

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The radius of the base of a right circular cone is increasing at the rate of \( 3 \mathrm{~cm} \) per minute and the altitude is decreasing at the rate of \( 4 \mathrm{~cm} \) per minute. Find the rate of change of total surface area of the cone when its radius is \( 7 \mathrm{~cm} \) and altitude is \( 24 \mathrm{~cm} \).
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