Concept explainers
(a)
The sum S8 of the volume of the cylinders.
(a)
Answer to Problem 20E
The value of S8 is 146.08406
Explanation of Solution
Given information:
Formula used:
The volume of cylinder is given by
Calculation:
Since hemisphere is approximated with cylinders.
So, volume of cylinder is given by
Here,
So, use LRAM with
And interval [0, 4] which is partitioned into eight equal subintervals so, length of a subinterval is 0.5 so, substitutes the value of x with 0.5 differences in f(x) from 0, 0.5.... up to 3.5 and then add and multiply with 0.5 then it is equal to S8
S8 is an overestimate because each rectangle is above the curve.
Conclusion:
The value of S8 is 146.08406
(b)
The percentage of V to the nearest percentage.
(b)
Answer to Problem 20E
The percentage error is 8.98%.
Explanation of Solution
Given information:
Formula used:
The Volume of hemisphere is
Calculation:
Volume of hemisphere is calculated as
Now, for percentage error
Conclusion:
The percentage error is 8.98%
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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