At what rate is the volume of the cube changing if the edge is 8cm and is changing at 4cm/sec
Solution;
Given;
a=8cm
dadt=4cm/s\frac{da}{dt}=4cm/sdtda=4cm/s
Since ;
V=a3V=a^3V=a3
dVdt=ddt(a3)\frac{dV}{dt}=\frac{d}{dt}(a^3)dtdV=dtd(a3)
dVdt=3a2dadt\frac{dV}{dt}=3a^2\frac{da}{dt}dtdV=3a2dtda
By direct substitution;
dVdt=3(82)(4)\frac{dV}{dt}=3(8^2)(4)dtdV=3(82)(4)
dVdt=768cm3/s\frac{dV}{dt}=768cm^3/sdtdV=768cm3/s
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