Concept explainers
i.
To find the volume of the cylinder, in terms of pi.
i.
Answer to Problem 15E
The volume of the cylinder- 47728 in3.
Explanation of Solution
Given:
The diameter of cylinder is 40 inches (d) and height is 38 inches.
Formula Used:Volume of cylinder is,
Calculation:
Since diameter of cylinder is 40 inches, therefore,
Radius (r)=
= 20 inches.
Substituting values of radius and height
Hence, volume of cylinder is
15200p inch3-----------------------(1)
Conclusion:
Volume of cylinder is
ii.
To find the volume of top cone and bottom cone, in terms of pi.
ii.
Answer to Problem 15E
volume of top cone is
Explanation of Solution
Given:
The diameter of top cone and bottom cone is same, that is, 40 inches (d). The height of top cone is 10 inches (h) and height of bottom cone is 8 inches (h).
Formula Used:Volume of a cone,
Calculation:
Since diameter of cylinder is 40 inches, therefore,
Radius (r)=
= 20 inches.
For top cone:
Substituting the values of radius and height,
Hence, the volume of top cone is:
For bottom cone:
Substituting the values of radius and height,
Hence, the volume of top cone is:
Conclusion:
The volume of top cone is
iii.
To find the total volume of the composter
iii.
Answer to Problem 15E
volume of the composter is 55263.96 inch3
Explanation of Solution
Given:
The volume of cylinder, top and bottom cones
Formula Used:
Volume of cone is,
Volume of cylinder is,
Calculation:
Volume of composter = volume of cylinder (1) + volume of top cone (2) - volume of bottom cone (3)
Substituting the values of (1), (2) and (3),
Hence, the volume of composter
Conclusion:
The volume of composter is 55263.96 inch3.
iv.
TO-DETERMINE that which whether radius affect the volume more or height.
iv.
Answer to Problem 15E
The radius has a greater effect on the volume of the composter.
Explanation of Solution
Since the radius must besquared in the volume formula of both cone and cylinder so reducing radius will make a greater impact on the volume.
Conclusion: The radius has a greater impact on the volume.
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