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Chapter 1: Problem 33

The pyramid described in Problem 32 contains approximately 2 million stone blocks that average 2.50 tons each. Find the weight of this pyramid in pounds.

Short Answer

Expert verified
The weight of the pyramid is approximately 10 billion pounds.

Step by step solution

01

Identify the given values

First identify the given values. The number of stone blocks in the pyramid is 2 million, and the average weight of each block is 2.50 tons.
02

Convert tons to pounds

The next step is to convert the weight from tons to pounds as the question asks for the answer in pounds. The conversion from tons to pounds is such that 1 ton equals 2000 pounds. Therefore, the weight of each stone block is \(2.50 \times 2000 \) pounds.
03

Calculate the total weight

To find the total weight of all the blocks, multiply the weight of each block (in pounds) by the total number of blocks. The total weight of the pyramid is \( 2,000,000 \times 2.50 \times 2000 \) pounds.

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Key Concepts

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

Weight Calculation
Weight calculation is an essential skill, especially when dealing with large structures, such as pyramids. In the exercise, we are tasked with determining the total weight of a pyramid made up of multiple stone blocks. By first identifying the average weight of a single block, which is given as 2.50 tons, and the total number of blocks, which is 2 million, you can calculate the total weight accurately. The formula involves multiplying these two values, but you need to ensure that the units are consistent. Since the final answer demands pounds, a conversion from tons to pounds is necessary. Always double-check units to avoid any mistakes.
Stone Blocks
Stone blocks are the fundamental building units of many ancient structures like pyramids. In physical terms, a block's weight influences the stability and durability of the entire structure. In the given exercise, each stone block weighs an average of 2.50 tons. To understand this better:
  • The volume and density of a stone typically determine its tonnage.
  • Different types of stones, such as limestone or granite, can have varied densities, affecting block weight.
  • When these stones accumulate, they form the colossal structures we see historically, like the Great Pyramids.
Grasping the concept of stone blocks and their weight helps to appreciate the engineering marvels achieved by civilizations using them.
Pyramid Structures
Pyramid structures are architectural feats characterized by their massive size and geometric shape. They are constructed by strategically stacking stone blocks, which necessitates a thorough understanding of weight and balance. Pyramids like those in Egypt, often involve:
  • Multiple layers of stone blocks, set in decreasing size as they approach the top.
  • Ingenious techniques to move and place heavy stones, considering both their dimensions and mass.
  • Architectural designs focusing on stability to prevent collapse under substantial weight.
As you explore pyramid structures, it's essential to remember the significance of weight calculations and unit conversions in ensuring structural integrity.
Physics Problems
Physics problems, such as calculating the weight of a pyramid from stone blocks, illustrate the practical application of physics in real-world scenarios. Key aspects to consider include:
  • The principle of weight as a vector, pointing towards the center of the Earth.
  • The importance of accurate measurements and unit conversions for credible results.
  • Application of multiplication and conversion techniques to solve problems effectively.
By working through problems like the one given, you get a glimpse into how physics melds with mathematical operations to solve tangible engineering challenges.

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Most popular questions from this chapter

\- Two spheres are cut from a certain uniform rock. One has radius \(4.50 \mathrm{cm} .\) The mass of the other is five times greater. Find its radius.

In a situation where data are known to three significant digits, we write \(6.379 \mathrm{m}=6.38 \mathrm{m}\) and \(6.374 \mathrm{m}=6.37 \mathrm{m}\) When a number ends in \(5,\) we arbitrarily choose to write \(6.375 \mathrm{m}=6.38 \mathrm{m} .\) We could equally well write \(6.375 \mathrm{m}=\) \(6.37 \mathrm{m},\) "rounding down" instead of "rounding up," because we would change the number 6.375 by equal increments in both cases. Now consider an order-of-magnitude estimate, in which we consider factors rather than increments. We write \(500 \mathrm{m} \sim 10^{3} \mathrm{m}\) because 500 differs from 100 by a factor of 5 while it differs from 1000 by only a factor of \(2 .\) We write \(437 \mathrm{m} \sim 10^{3} \mathrm{m}\) and \(305 \mathrm{m} \sim 10^{2} \mathrm{m}\) What distance differs from \(100 \mathrm{m}\) and from \(1000 \mathrm{m}\) by equal factors, so that we could equally well choose to represent its order of magnitude either as \(\sim 10^{2} \mathrm{m}\) or as \(\sim 10^{3} \mathrm{m} ?\)

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The consumption of natural gas by a company satisfies the empirical equation \(V=1.50 t+0.00800 t^{2},\) where V is the volume in millions of cubic feet and \(t\) the time in months. Express this equation in units of cubic feet and seconds. Assign proper units to the coefficients. Assume a month is equal to 30.0 days.
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