/*! 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 46 A unit of area often used in mea... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 46

A unit of area often used in measuring land areas is the hectare, defined as \(10^{4} \mathrm{~m}^{2}\). An open-pit coal mine consumes 75 hectares of land, down to a depth of \(26 \mathrm{~m},\) each year. What volume of earth, in cubic kilometers, is removed in this time?

Short Answer

Expert verified
0.0195 cubic kilometers

Step by step solution

01

Convert Hectares to Square Meters

First, recognize that a hectare is a measure of area defined as \(10^4\) square meters. Since the mine consumes 75 hectares, we convert this to square meters by calculating \(75 \text{ hectares} \times 10^4 \text{ m}^2/\text{hectare} = 75 \times 10^4 \text{ m}^2 = 750,000 \text{ m}^2\).
02

Calculate the Volume in Cubic Meters

The volume of earth removed is the area of the land multiplied by the depth of the mine. Thus, the volume is \(750,000 \text{ m}^2 \times 26 \text{ m} = 19,500,000 \text{ m}^3\).
03

Convert Cubic Meters to Cubic Kilometers

Since there are \(10^9\) cubic meters in a cubic kilometer, we convert the volume from cubic meters to cubic kilometers. The conversion is \(\frac{19,500,000 \text{ m}^3}{10^9 \text{ m}^3/\text{km}^3} = 0.0195 \text{ km}^3\).

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.

Measurement of Land Area
Understanding how land area is measured is essential, especially when dealing with large-scale projects like mining or agriculture. A common unit of land measurement is the hectare. The hectare is an area unit equivalent to 10,000 square meters, making it suitable for quantifying extensive tracts of land. - A 'hectare' is useful because it covers large areas, larger than an acre, which is about 2.47 times smaller than a hectare. In our exercise, the mine covers 75 hectares. To understand the scale, multiplying the number of hectares by the number of square meters in one hectare gives us the total area in square meters. Here: - 75 hectares x 10,000 square meters per hectare = 750,000 square meters. This conversion is crucial as square meters are the standard metric unit for expressing area, allowing easier integration into further calculations involving volume.
Volume Calculation
When determining how much material is being moved, understanding how to calculate volume is essential. Volume can be thought of as the measure of space occupied by a three-dimensional object, such as the body of earth being mined.To calculate volume, if you know the area and depth:- Area (in square meters) x Depth (in meters) = Volume (in cubic meters).Applying this to our example:- With an area of 750,000 square meters and a depth of 26 meters, the volume is calculated as follows: \[750,000 ext{ m}^2 \times 26 ext{ m} = 19,500,000 ext{ m}^3.\]This volume represents the total amount of earth taken from the mine annually, measured initially in cubic meters, the most straightforward metric volume unit.
Cubic Kilometers Conversion
The step from cubic meters to cubic kilometers involves converting a smaller unit to a larger one. Cubic meters are standard for day-to-day or small-scale volume calculations, but for enormous quantities, cubic kilometers facilitate comprehension and comparison.- One cubic kilometer equals a billion (1,000,000,000) cubic meters, or \(10^9\) cubic meters.To carry out this conversion, take the volume in cubic meters and divide by the number of cubic meters per cubic kilometer:- \[\frac{19,500,000 ext{ m}^3}{1,000,000,000 ext{ m}^3/ ext{km}^3} = 0.0195 ext{ km}^3.\]This conversion shows that the volume removed in one year is 0.0195 cubic kilometers. This small, digestible number makes it easy to assess and communicate significant quantities in contexts like land management or environmental impact discussions.

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

For about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What are the ratios of (a) the French decimal week to the standard week and (b) the French decimal second to the standard second?

The cubit is an ancient unit of length based on the distance between the elbow and the tip of the middle finger of the measurer. Assume that the distance ranged from 43 to \(53 \mathrm{~cm},\) and suppose that ancient drawings indicate that a cylindrical pillar was to have a length of 9 cubits and a diameter of 2 cubits. For the stated range, what are the lower value and the upper value, respectively, for (a) the cylinder's length in meters, (b) the cylinder's length in millimeters, and (c) the cylinder's volume in cubic meters?

A gry is an old English measure for length, defined as \(1 / 10\) of a line, where line is another old English measure for length, defined as \(1 / 12\) inch. A common measure for length in the publishing business is a point, defined as \(1 / 72\) inch. What is an area of \(0.50 \mathrm{gry}^{2}\) in points squared (points \(^{2}\) )?

In purchasing food for a political rally, you erroneously order shucked medium-size Pacific oysters (which come 8 to 12 per U.S. pint) instead of shucked medium-size Atlantic oysters (which come 26 to 38 per U.S. pint \() .\) The filled oyster container shipped to you has the interior measure of \(1.0 \mathrm{~m} \times 12 \mathrm{~cm} \times 20 \mathrm{~cm},\) and a U.S. pint is equivalent to 0.4732 liter. By how many oysters is the order short of your anticipated count?

Spacing in this book was generally done in units of points and picas: 12 points \(=1\) pica, and 6 picas \(=1\) inch. If a figure was misplaced in the page proofs by \(0.80 \mathrm{~cm},\) what was the misplacement in (a) picas and (b) points?
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Scientific Method Physics

Read Explanation

Famous Physicists

Read Explanation

Electricity

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.