Question

help me to solve this:
A block of ice in the shape of a cube originally having volume 1000cm3 is melting in such way that the
length of each of its edges is decreasing at the rate of 2cm/hr. At what rate is its surface area decreasing at
the time its volume is 64cm3? Assume that the block of ice maintains its cubical shape? [ans: -96cm2/hr]
show me the full solution.

Answer 1

Let s be length of an edge.
\[V = s^{3}\]
\[SA = 6s^{2}\]
\[\frac{ds}{dt} = -2\]
Find dA/dt, where dA refers to change in surface area
\[\frac{dA}{dt} = \frac{ds}{dt}*\frac{dA}{ds}\]
\[\frac{dA}{ds} = 12s\]
\[\frac{dA}{dt} = (-2)(12s) = -24s\]
We want the rate when V=64, find the s that gives a volume of 64
\[s^{3} = 64\rightarrow s = 4\]
\[\frac{dA}{dt} = -24*4 = -96\]

Answer 2

thanks..

Answer 3

no problem

Answer 4

can i know, how about the volume 1000cm^3 given?