(a)
The area of the cross sections corresponding to the given circumferences.
(a)
Answer to Problem 78E
The area of the cross sections has been find out.
Explanation of Solution
Given:
The height of the vase measured is
Calculation:
Circumference can be find out as;
Now, the formula to find out area is as follows:
S.no. | Height (in inches) | Circumference (in inches) | Radius (in inches) | Area ( in inches2) |
0 | 0 | 5.4 | 0.8594 | 2.3205 |
1 | 0.5 | 4.5 | 0.7162 | 1.6114 |
2 | 1 | 4.4 | 0.7003 | 1.5406 |
3 | 1.5 | 5.1 | 0.8117 | 2.0698 |
4 | 2 | 6.3 | 1.0027 | 3.1584 |
5 | 2.5 | 7.8 | 1.2414 | 4.8415 |
6 | 3 | 9.4 | 1.4961 | 7.0315 |
7 | 3.5 | 10.8 | 1.7189 | 9.2819 |
8 | 4 | 11.6 | 1.8462 | 10.7079 |
9 | 4.5 | 11.6 | 1.8462 | 10.7079 |
10 | 5 | 10.8 | 1.7189 | 9.2819 |
11 | 5.5 | 9 | 1.4324 | 6.4458 |
12 | 6 | 6.3 | 1.0027 | 3.1584 |
Conclusion:
The area of cross sections has been find out.
(b)
The volume of a vase.
(b)
Answer to Problem 78E
The volume of a vase is
Explanation of Solution
Given:
n=12
Calculation:
The volume of an element of a vase can be find out as:
Now, to calculate the volume of a vase can be obtained by integrating the volume of an element.
Hence, Volume can be find out as:
Conclusion:
The volume of a vase is
(c)
The value of integral using trapezoidal rule.
(c)
Answer to Problem 78E
The approximate volume using trapezoidal rule is
Explanation of Solution
Given:
The interval is given
Calculation:
The volume of an element of a vase can be find out as:
Now, to calculate the volume of a vase can be obtained by integrating the volume of an element.
Conclusion:
The approximate volume using trapezoidal rule is
Chapter 7 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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