Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 15

Antarctica is roughly semicircular in shape with a radius of \(2000 \mathrm{~km}\). The average thickness of the ice cover is \(3000 \mathrm{~m}\). How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of the Earth.)

Short Answer

Expert verified
The volume of ice that Antarctica contains is \( V = \frac{2}{3} * \pi * (300000)^3 \) cubic centimeters. Calculate the expression to get the final numerical value.

Step by step solution

01

Data Conversion

The radius r is given in kilometers and needs to be converted into centimeters. We know that 1 km = 100000 cm. So, \( r = 2000 * 100000 = 200000000 \) cm. Similarly, convert the thickness from meters to centimeters. Therefore, \( thickness = 3000 * 100 = 300000 \) cm. To find the volume of ice, the thickness will be used as the radius.
02

Calculation of Volume

Now that we have the radius, we can use the volume formula to calculate the volume of the hemisphere. Using the volume formula \( V = \frac{2}{3} * \pi * r^3 \), where r = 300000 cm, we get \( V = \frac{2}{3} * \pi * (300000)^3 \).
03

Simplifying the Result

Solving the expression will give us the volume of the ice in cubic centimeters.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Astronomical distances are so large compared to terrestrial ones that much larger units of length are used for easy comprehension of the relative distances of astronomical objects. An astronomical unit \((\mathrm{AU})\) is equal to the average distance from Earth to the Sun, \(1.50 \times 10^{8} \mathrm{~km}\). A parsec (pc) is the distance at which 1 AU would subtend an angle of 1 second of arc. A light-year (ly) is the distance that light, traveling through a vacuum with a speed of \(3.00 \times 10^{5} \mathrm{~km} / \mathrm{s}\), would cover in 1 year. ( \(a\) ) Express the distance from Earth to the Sun in parsecs and in light-years. (b) Express a light-year and a parsec in kilometers. Although the light-year is much used in popular writing, the parsec is the unit preferred by astronomers.

Assuming that the length of the day uniformly increases by \(0.001 \mathrm{~s}\) in a century, calculate the cumulative effect on the measure of time over 20 centuries. Such a slowing down of the Earth's rotation is indicated by observations of the occurrences of solar eclipses during this period.

A certain pendulum clock (with a 12 -h dial) happens to gain 1 min/day. After setting the clock to the correct time, how long must one wait until it again indicates the correct time?

The time it takes the Moon to return to a given position as seen against the background of fixed stars, \(27.3\) days, is called a sidereal month. The time interval between identical phases of the Moon is called a lunar month. The lunar month is longer than a sidereal month. Why and by how much?

Porous rock through which groundwater can move is called an aquifer. The volume \(V\) of water that, in time \(t\), moves through a cross section of area \(A\) of the aquifer is given by $$ V / t=K A H / L $$ where \(H\) is the vertical drop of the aquifer over the horizontal distance \(L\); see Fig. \(1-5 .\) This relation is called Darcy's law. The quantity \(K\) is the hydraulic conductivity of the aquifer. What are the SI units of \(K ?\)
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Dynamics

Read Explanation

Mechanics and Materials

Read Explanation

Torque and Rotational Motion

Read Explanation

Classical Mechanics

Read Explanation

Conservation of Energy and Momentum

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.

Sign-up for free