Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 63, Problem 13A

A vessel is in the shape of a right circular cone. This vessel contains liquid to a depth of 12.8 centimeters, as shown. How many liters of liquid must be added in order to fill the vessel? One liter contains 1000 cubic centimeters.
Chapter 63, Problem 13A, A vessel is in the shape of a right circular cone. This vessel contains liquid to a depth of 12.8

Expert Solution & Answer
Check Mark
To determine

The amount of liquid needs to be added to fill the vessel completely.

Answer to Problem 13A

  0.80L

Explanation of Solution

Given:

  Mathematics For Machine Technology, Chapter 63, Problem 13A

Concept used:

The volume of a right circular cone is

  V =13ABh

Where, h = height, and AB = Base area.

Calculation:

The base area is Ab=πr2

Now, the base area of the cone is

  Ab=3.14×( D 2)2[r=D2]Ab=3.14×( 15 2)2Ab=3.14×(7.5)2Ab=176.625cm2

The total volume of the vessel is

  V =13×176.625×19.2V =3391.23V=1130.4cm3

Now, the base area of cone up to it contains liquid is

  Ab1=3.14×( D 1 2)2[r=D2]Ab1=3.14×( 10 2)2Ab1=3.14×(5)2Ab1=78.5cm2

The volume of the vessel is

  V1 =13×78.5×12.8V1 =1004.83V1=335cm3

Thus, the remaining amount of liquid that is needed to fill the vessel is

  Vr = Total volume − volume of vessel up to it contains liquid

  Vr =V-V1or,Vr =1130.4-335Vr = 795.4cm3

Thus, the amount of liquid is to be added in liters is

  Vr =795.41000or,Vr =0.790.80Vr =0.80L

Conclusion:

Hence, the amount of liquid is 0.80 L.

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