Question #322988

At what rate is the volume of the cube changing if the edge is 8cm and is changing at 4cm/sec

1
Expert's answer
2022-04-04T14:26:34-0400

Solution;

Given;

a=8cm

dadt=4cm/s\frac{da}{dt}=4cm/s

Since ;

V=a3V=a^3

dVdt=ddt(a3)\frac{dV}{dt}=\frac{d}{dt}(a^3)

dVdt=3a2dadt\frac{dV}{dt}=3a^2\frac{da}{dt}

By direct substitution;

dVdt=3(82)(4)\frac{dV}{dt}=3(8^2)(4)

dVdt=768cm3/s\frac{dV}{dt}=768cm^3/s


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