Answer:
[tex]\frac{ds}{dt} =31.952[/tex]
Step-by-step explanation:
From the question we are told that
Cube increase rate 459 cubic inches
At 408
Generally the expressions of the is mathematically given to be
[tex]\frac{dv}{dt} =459[/tex]
[tex]\frac{dv}{dt} =3*l^2 \frac{dl}{dt}[/tex]
[tex]v=408[/tex]
Generally
[tex]v=l^3[/tex]
Therefore solving Mathematically
[tex]\frac{dv}{dt} =3*l^2 \frac{dl}{dt}[/tex]
[tex]459 =3*(7.416859539)^2 \frac{dl}{dt}[/tex]
[tex]459 =165.0294163\frac{dl}{dt}[/tex]
[tex]\frac{dl}{dt} =\frac{165.0294163}{459}[/tex]
[tex]\frac{dl}{dt} =0.359[/tex]
Therefore solving mathematically for surface area
[tex]Surface area S=6l^2[/tex]
[tex]\frac{ds}{dt} =6(2l* \frac{dl}{dt})[/tex]
[tex]\frac{ds}{dt} =12l* \frac{dl}{dt}[/tex]
[tex]\frac{ds}{dt} =12*(7.416859539)*0.359[/tex]
[tex]\frac{ds}{dt} =31.95183089[/tex]
[tex]\frac{ds}{dt} =31.952[/tex]
