Concept explainers
a.
To find: The Riemann sum that approximates the force exerted on the entire front of the tank.
a.
Answer to Problem 4QQ
The Riemann sum is
Explanation of Solution
Given:
The breadth and height of the tank is
Calculation:
The Riemann sum that approximates the force exerted on the entire front of the tank can be calculated by taking the expression for pressure, and evaluating the sum over the ranges.
We have to divide
Thus,
Therefore, the Riemann sum is
b.
To find: The definite
b.
Answer to Problem 4QQ
The definite integral that gives the force exerted on the front of the tank is
Explanation of Solution
Given:
The breadth and height of the tank is
Calculation:
To find the definite integral that gives the force exerted on the front of the tank we have to convert The Riemann integral into an integral by taking limit
Hence,
Therefore, the definite integral that gives the force exerted on the front of the tank is
c.
To find: The total force exerted on the front the tank if the front are semicircles with diameter two feet.
c.
Answer to Problem 4QQ
The total force is
Explanation of Solution
Given:
The information is given above.
Calculation:
Here, the equation of the semicircle with respect to height is given by,
Now, from the part b our integral becomes,
Therefore, the total force is
Chapter 8 Solutions
Calculus: Graphical, Numerical, Algebraic
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