a.
Find a formula for the volume
a.
Answer to Problem 64E
The volume of cone is
Explanation of Solution
Given:
A circular disk of radius
Also, given that the cone is constructed by removing a sector
Concept used:
Circumference of circle of radius
Calculation:
Circumference of circular disk of radius
Circumference of circular disk by removing a sector
The circumference of base of cone with height
As given that the cone is constructed by removing a sector
Height of cone in the form of
In triangle
Volume of cone:
Conclusion:
The volume of cone is
b.
Find the
b.
Answer to Problem 64E
The values of radius and height :
4 | 3.265 | 2.309 |
5 | 4.082 | 2.887 |
6 | 4.899 | 3.464 |
8 | 6.532 | 4.619 |
Explanation of Solution
Given:
Radius of cone:
Height of cone:
Volume of cone:
Values of
Calculation:
Case 1:- when
Volume of cone:
Put
Draw the graph of
Here,
Now, according to graph
Case 1:- when
Put
Radius of cone:
Height of cone:
Case 2:- when
Put
Radius of cone:
Height of cone:
So,
Similarly, solve for the remaining values of
4 | 3.265 | 2.309 |
5 | 4.082 | 2.887 |
6 | 4.899 | 3.464 |
8 | 6.532 | 4.619 |
c.
Find a relation between
c.
Answer to Problem 64E
The relation between radius
Explanation of Solution
Calculation:
Given that,
In triangle
Also, volume of cone:
Simplify it,
For
Put
Now,
This is the relation between radius
To get this relation first write the radius
For maximum value of volume differentiate the equation. Now simplify it for relation.
Conclusion:
The relation between radius
Chapter 4 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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