A class measured the radius r, circumference C, and area A of various circular objects. The results are recorded in this table. Does there appear to be a proportional relationship between circumference and area?
Answers
Answer:
hope it helps
Step-by-step explanation:
The area of a circle is given by the formula A = π r2, where A is the area and r is the radius. The circumference of a circle is C = 2 π r. If we "solve for r" in the second equation, we have r = C / (2 π ). ... When we simplify this, we get A = C2 / (4 π)
Answer:
Work through all of the exercises, then take the quiz and submit it to be graded. The grade for the lab is based entirely on the quiz, so be sure that you understand the exercise and the learning outcomes.
Background Information on Lab 3
Computer Notation
Contents
Introduction
Outcomes
Supplies
Procedure 1
Procedure 2
Procedure 3
Questions
1. INTRODUCTION
A graph is a pictorial representation of ordered pairs of numbers. The reader can quickly determine relationships between quantities that the ordered pairs represent.
In many of the experiments performed in our laboratory exercises, we will study quantities that change in value. A change in one quantity may cause another quantity to change. We say one quantity is a FUNCTION of the other. For example, the area of a circle is a FUNCTION of the radius. That is, the area depends on the size of the radius in a regular and predictable way. When we increase the size of the radius the area of the circle increases accordingly. In this example the radius is called the INDEPENDENT VARIABLE and the area is the DEPENDENT VARIABLE.
A graph is plotted as a picture of ordered pairs of numbers where one number is related to another by a specific relationship, sometimes incorrectly called a formula. To draw a graph we use graph paper and a set of ordered pairs of numbers. Spreadsheet programs such as Excel have the capability to draw graphs and determine the relationship between the ordered pairs.
The ordered pairs of numbers might be calculated or determined by measurements,
In this exercise, you will determine the ordered pairs and plot graphs using the mathematical relationship for the circumference of a circle as a function of the diameter of the circle, and the area of a circle as a function of its radius.
The pairs of points, representing different values of the variables, will be plotted on graph paper or with computer software. The plotted points will connected by a smooth line that may be straight or it may be curved depending on the type of relationship that the ordered pairs represent. The general name "CURVE" is used in reference to all graphs whether the line is actually curved or straight.
Key Points to Note
The constant of proportion of a linear relationship is the same number as the slope of the graph that plots the relationship.
Definition: constant of proportion - the constant value of the ratio of two proportional quantities x and y; usually written y/x = k or y = kx, where k is the constant of proportion.
See "Direct Proportion"
In this exercise you will explore the connections between numbers, symbolic notation (otherwise known as equations) and graphs.
2. LEARNING OUTCOMES
After completing this exercise you should be able to do the following:
Define and explain the term "graph
Plot a proper graph of a linear relationship.
Label and name a properly drawn graph.
Plot a graph of a nonlinear relationship using a mathematical equation to obtain ordered pairs of numbers.
Distinguish between dependent and independent variables.
Define slope, determine the slope of a straight line, and equate the slope with the constant of proportion.
State the symbolic relationship for a straight line
State the general form of the relationship for a parabola.
Replot a parabola as a straight line.
3. EQUIPMENT AND SUPPLIES
pencil, ruler, calculator, graph paper
Drawing software may be used to draw graphs but it is not necessary
Computer graphing software may be used but is not necessary*
Chapter 5 in the Booth & Bloom text is be a useful reference
See web sites for computer graphing
4. PROCEDURE 1: Circumference vs. Diameter
In this procedure you will see the relationship between "ratio", "constant of proportion", and "slope" of a linear graph.
The number known as "pi" occurs frequently in calculations involving circles and circular motion. It is an irrational number that represents the constant ratio between the circumference and diameter of a circle.
Relationship 4.1
The number 'pi' () is the ratio of the circumference of a circle to its diameter. It is the same for all circles because all circles are the same shape. The value of pi is approximately 3.14.
C= x D
where C = the circumference,
D = the diameter,
= 3.14
4.1. COMPLETE DATA TABLE 1.1.
Multiply each of the values in the diameter column (independent) by to calculate the value in the circumference (dependent) column.
1. Round off the calculated circumferences to two decimal places.
2. Complete the ratio (C/D) column by dividing the number in the circumference (C) column by the number in the same row of the diameter (D) column.