Assume that a snowball melts in such a way that its volume decreases at a rate proportional to its surface area. If half the original snowball has melted away after 2 hours, how much longer will it take for the snowball to disappear completely? (Answer = (2/(cuberoot(2) - 1)) or 7.69 hours)
2026-04-01 00:27:24.1775003244
Related Rates- Snowball Melting...
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Let r be radius, then (dr/dt) = ((r^3)/2) * (1 - (1/ cube root(2)). Volume of sphere is proportional to radius. Therefore, the volume will diminish to zero after x hours: r^3 - (r^3/2)*{(1 - 1/(cube root 2))}*x = 0. X - 2 equals what you have.
Let r be radius, then ${dr \over dt}$ = $ r^3 \over 2$ * (1 - $1 \over (\sqrt[3]{2})$). Volume of sphere is proportional to radius. Therefore, the volume will diminish to zero after x hours: $ r^3$ - $ r^3 \over 2$ * (1 - $1 \over (\sqrt[3]{2})$)*x. x - 2 equals what you have.