Question: In Worked Example 4.1 , it is easy enough to measure the width of a pyramid. To measure the height without climbing to the top,
In Worked Example 4.1 , it is easy enough to measure the width of a pyramid. To measure the height without climbing to the top, you can use a theodolite and determine the angle between the ground and the line joining the theodolite’s position and the top of the pyramid. What other information do you need in order to compute the surface area?
Data from worked example 4.1.
WORKED EXAMPLE 4.1 Computing the Volume and Surface Area of a Pyramid In this worked Example, we develop a solution to a computational problem. Problem Statement Suppose that you are helping archaeologists who research Egyptian pyramids. You have taken on the task of writing a method that determines the volume and surface area of a pyramid, given its height and base length.
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In the worked example you are given a method to calculate the volume and surface area of a pyramid based on its height and base length To measure the height without climbing to the top you would be using a theodolite to determine the angle to the top of the pyramid from the ground However to calculate the surface area especially if you are not including the base in the total surface area as is the case in the example provided you need another important piece of information besides the base length the slant height of the pyramid The slant height is the distance from the top of the pyramid to any point on the edge of the base along the pyramids face However if you cannot directly measure the slant height you can still compute it if you know the height of the pyramid and the base length According to the third image provided the surface area A of the pyramid without the base is calculated using the formula A 2bs Where b is the base length s is the slant height The slant height can be calculated using the Pythagorean theorem if the pyramid is a right pyramid with a square base In a right pyramid the slant height the height from the center of the base to the apex and half the base form a right triangle Thus you can use the relationship s2 h2 b22 Where h is the height of the pyramid b ... View full answer
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