Answer:
D. 348
Step-by-step explanation:
The volume of the square prisma is given by the following formula:
[tex]V = s^{2}h[/tex]
In which h is the height, and s is the side of the base.
Let's use implicit derivatives to solve this problem:
[tex]\frac{dV}{dt} = 2sh\frac{ds}{dt} + s^{2}\frac{dh}{dt}[/tex]
In this problem, we have that:
[tex]\frac{ds}{dt} = 5, \frac{dh}{dt} = -2, h = 7, s = 6[/tex]
So
[tex]\frac{dV}{dt} = 2sh\frac{ds}{dt} + s^{2}\frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt} = 2*6*7*5 + (6)^{2}*(-2) = 348[/tex]
So the correct answer is:
D. 348
