Finding the volume of the pyramid and also determining the increase and decrease of its...

Addison Trujillo

Addison Trujillo

Answered

2022-07-14

Finding the volume of the pyramid and also determining the increase and decrease of its volume
The volume of a pyramid with a square base x units on a side and a height of h is V = 1 3 x 2 h.
1) Suppose x = e t and h = e 2 t . Use the chain rule to find V 1 ( t ).
2) Does the volume of the pyramid increase or decrease as t increases.

Answer & Explanation

furniranizq

furniranizq

Expert

2022-07-15Added 20 answers

Step 1
V = 1 3 e 2 t e 2 t = 1 3 e 2 t 2 t = 1 3 e 0 = 1 3
Thus V ( t ) = 0. But if you insist on using the chain rule then, we apply the product rule and then the chain rule
Step 2
V = 2 3 e 2 t e 2 t + 2 3 e 2 t e 2 t = 0
Clearly the volume of the pyramid clearly is a constant so doesn't increase or decrease.

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