/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 The Earth's surface is about \(7... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 37

The Earth's surface is about \(70 \%\) water. Mars's diameter is about half the Earth's, but it has no surface water. Compare the land areas of the two planets.(answer check available at lightandmatter.com)

Short Answer

Expert verified
Earth has more land than Mars because only 30% of Earth's larger surface is land, yet it still surpasses Mars's entire land area.

Step by step solution

01

Calculate the Earth's Surface Area

The surface area of a sphere is given by the formula \(A = 4 \pi r^2\). Let's denote the Earth's radius as \(r_e\) and Mars's radius as \(r_m = \frac{1}{2} r_e\). Using \(r_e = 1\) for simplicity, the surface area of Earth is \(A_e = 4 \pi (1)^2 = 4 \pi\).
02

Calculate Mars's Surface Area

Given that the radius of Mars is half that of Earth, \(r_m = \frac{1}{2}\), the surface area of Mars is \(A_m = 4 \pi \left(\frac{1}{2}\right)^2 = 4 \pi \cdot \frac{1}{4} = \pi\).
03

Calculate Earth's Land Area

Since \(70\%\) of Earth's surface is water, \(30\%\) is land. The land area \(L_e\) of Earth is \(L_e = 0.3 \times 4 \pi = 1.2 \pi\).
04

Compare the Land Areas

Since Mars has no water, its entire surface area is land, \(L_m = \pi\). Comparing Earth's land area \(1.2 \pi\) and Mars's land area \(\pi\): \(L_e = 1.2 \pi > L_m = \pi\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Surface Area Calculation
Calculating the surface area of a sphere is crucial to understanding the size and comparison of planetary bodies. The formula used to calculate the surface area of a sphere is given by
  • \( A = 4 \pi r^2 \)
where \( A \) represents the surface area and \( r \) is the radius of the sphere.On Earth, the radius is often simplified to \( r_e = 1 \) for ease of calculation, resulting in a surface area of \( A_e = 4 \pi \times (1)^2 = 4 \pi \). For Mars, given its radius is half of Earth's (\( r_m = \frac{1}{2} \)),
  • we adjust the formula to calculate the surface area: \( A_m = 4 \pi \left(\frac{1}{2}\right)^2 = 4 \pi \cdot \frac{1}{4} = \pi \).
These computations show how varying the radius influences surface area, a concept useful in comparing celestial bodies.
Earth and Mars
Earth and Mars share intriguing similarities and striking differences, primarily in size. Understanding these helps comprehend planetary characteristics better. Earth, with a larger diameter, results in a greater surface area compared to Mars, whose diameter is only half as much. Consequently, while Earth鈥檚 surface area is calculated as \( 4 \pi \), Mars鈥檚 comes out to be just \( \pi \). Despite physical size differences, this measurable data aids in comprehending planetary environments:
  • Earth offers diverse living conditions, primarily due to its significant surface area and water presence.
  • Mars鈥� smaller, barren surface with no present water reflects varied potential for exploration and habitation.
These comparisons convey how size and environment affect each planet differently, presenting distinct challenges and opportunities in space exploration.
Land and Water Distribution
On Earth, the distribution of land and water plays a significant role in its habitability. The planet is composed of about \( 70\% \) water, which influences the climate and supports life. Consequently, only \( 30\% \) of Earth's surface is land, calculated as \( L_e = 0.3 \times 4 \pi = 1.2 \pi \). Mars, in contrast, presents its entire surface as land due to the absence of surface water:
  • Thus, its land area is equivalent to its total surface area, \( L_m = \pi \).
Comparing these aspects:
  • Earth's diverse ecosystems thrive due to its significant water presence.
  • Mars lacks these conditions, making it less suitable for traditional life support.
Understanding these distributions highlights essential differences and considerations when assessing planetary habitability.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You are looking into a deep well. It is dark, and you cannot see the bottom. You want to find out how deep it is, so you drop a rock in, and you hear a splash \(3.0\) seconds later. How deep is the well? (answer check available at lightandmatter.com)

(solution in the pdf version of the book) How many \(\mathrm{cm}^{2}\) is \(1 \mathrm{~mm}^{2}\) ?

Assume a dog's brain is twice as great in diameter as a cat's, but each animal's brain cells are the same size and their brains are the same shape. In addition to being a far better companion and much nicer to come home to, how many times more brain cells does a dog have than a cat? The answer is not \(2 .\)

Correct use of a calculator: (a) Calculate \(\frac{74658}{53222+97554}\) on a calculator. [Self-check: The most common mistake results in 97555.40.] (answer check available at lightandmatter.com) (b) Which would be more like the price of a TV, and which would be more like the price of a house, \(\$ 3.5 \times 10^{5}\) or \(\$ 3.5^{5}\) ?

. The one-liter cube in the photo has been marked off into smaller cubes, with linear dimensions one tenth those of the big one. What is the volume of each of the small cubes?(solution in the pdf version of the book)
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Translational Dynamics

Read Explanation

Force

Read Explanation

Electricity and Magnetism

Read Explanation

Torque and Rotational Motion

Read Explanation

Particle Model of Matter

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.