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. 318

The volume of a square pnsm with base side s and neignth is s² h.

Question

Mathematics

Lorelai Butler

23 January, 03:34

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. 318

The volume of a square pnsm with base side s and neignth is s² h.

+4

Answers (1)

Know the Answer?

Brooks Duran · Answer 1

348

Step-by-step explanation:

348

Step-by-step explanation:

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

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

Let's use implicit derivatives to solve this problem:

In this problem, we have that:

So the correct answer is:

348