Question

The side of the base of a square prism is increasing at a rate of 5 meters per second and the height of the prism as decreasing at a rate of 2 meters per second. At a certain instant, the base's side is 6 meters and the height is 7 meters. What is the rate of change of the volume of the prism at that instant fin cubic meters per second?
A. -348
B. 492
C. -492
D. 348

Answer 1

Answer:

D. 348

Step-by-step explanation:

The volume of the square prisma is given by the following formula:

$V = s^{2}h$

In which h is the height, and s is the side of the base.

Let's use implicit derivatives to solve this problem:

$\frac{dV}{dt} = 2sh\frac{ds}{dt} + s^{2}\frac{dh}{dt}$

In this problem, we have that:

$\frac{ds}{dt} = 5, \frac{dh}{dt} = -2, h = 7, s = 6$

So

$\frac{dV}{dt} = 2sh\frac{ds}{dt} + s^{2}\frac{dh}{dt}$

$\frac{dV}{dt} = 2*6*7*5 + (6)^{2}*(-2) = 348$

So the correct answer is:

D. 348