Answer to Question #322988 in Calculus for josh

Question

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

Answer 1

Solution;

Given;

a=8cm

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

Since ;

$V=a^3$

$\frac{dV}{dt}=\frac{d}{dt}(a^3)$

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

By direct substitution;

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

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