(a) Explanation Write the expression to calculate the density. ρ = m V (I) Here, ρ is the density, m is the mass and V is the volume. Rewrite the above expression for mass. m = ρ V (II) Write the expression to calculate the volume of the outer core. V OC = V CO − V I (III) Here, V OC is the volume of the outer core, V CO is the total volume including the inner core and the outer core, and V I is the volume of the inner core. Write the expression to calculate the volume of the mantle. V M = V CM − V CO (IV) Here, V M is the volume of the mantle, V CM is the total volume including the inner core, the outer core and the mantle. Write the expression to calculate the volume. V = 4 3 π r 3 (V) Here, r is the radius. Conclusion: Substitute 1220 km for r in equation (V) to calculate the volume of the inner core. ` V I = 4 3 π ( 1220 km ) 3 = 4 3 π ( 1220 km ( 1000 m 1 km ) ) 3 = 7.6 × 10 18 m 3 Substitute 3480 km for r in equation (V) to calculate the volume including the inner core and the outer core. ` V CO = 4 3 π ( 3480 km ) 3 = 4 3 π ( 3480 km ( 1000 m 1 km ) ) 3 = 176.53 × 10 18 m 3 Substitute 6371 km for r in equation (V) to calculate the volume including the inner core, the outer core and the mantle. ` V CM = 4 3 π ( 6371 km ) 3 = 4 3 π ( 6371 km ( 1000 m 1 km ) ) 3 = 1083.21 × 10 18 m 3 Substitute 176.53 × 10 18 m 3 for V CO and 7 (b) To determine The actual average density of the entire Earth and to compare it with the density obtained in subpart (a).

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Density of Solids

The density of a substance refers to how much matter is present in a given amount of space. It is expressed as the ratio of the mass of the substance to its volume.

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Chapter 13, Problem 7P

(a)

To determine

The average density of the entire earth based on the model of the Earth.

(b)

To determine

The actual average density of the entire Earth and to compare it with the density obtained in subpart (a).

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Chapter 13, Problem 6P

Chapter 13, Problem 8P

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Chapter 13 Solutions

Physics for Scientists and Engineers with Modern Physics

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The average density of the entire earth based on the model of the Earth.

Solution Summary: The author explains how to calculate the density, mass, and volume of the earth. Substitute 1220km for r.

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The average density of the entire earth based on the model of the Earth.

The actual average density of the entire Earth and to compare it with the density obtained in subpart (a).

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Chapter 13 Solutions