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Chapter 13: Problem 8

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ \text {The circumference of a circular region with radius \(r\)} & \text {The perimeter of a square with side \(r\) }\end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
a. Quantity A is greater.

Step by step solution

01

Write down the Formula for the Circumference of a Circle

The formula for the circumference of a circle is \(C = 2\pi r\). So, if the radius is \(r\), the circumference would be \(2\pi r\). This is also known as Quantity A.
02

Write down the Formula for the Perimeter of a Square

The formula for the perimeter of a square is \(P = 4s\), where \(s\) is the length of one side of the square. If the length of the side is \(r\), then the perimeter becomes \(4r\). This is also known as Quantity B.
03

Compare Quantities A and B

Now compare Quantity A (\(2\pi r\)) and Quantity B (\(4r\)). It can be observed that \(2\pi r\) is greater than \(4r\) since \(2\pi\) (approximately 6.28) is greater than 4. Therefore, Quantity A is greater than Quantity B.

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Most popular questions from this chapter

For the final exam in a scuba diving certification course, Karl navigates from one point in a lake to another. Karl begins the test \(x\) meters directly beneath the boat and swims straight down toward the bottom of the lake for 8 meters. He then turns to his right and swims in a straight line parallel to the surface of the lake and swims 24 meters, at which point he swims directly from his location, in a straight line, back to the boat. If the distance that Karl swims back to the boat is 26 meters, what is the value of \(x ?\)

Which of the following could be the degree measures of two angles in a right triangle? Indicate all such angles. A. \(20^{\circ}\) and \(70^{\circ}\) B. \(30^{\circ}\) and \(60^{\circ}\) C. \(45^{\circ}\) and \(45^{\circ}\) D. \(55^{\circ}\) and \(55^{\circ}\) E. \(75^{\circ}\) and \(75^{\circ}\)

Triangle \(A B C\) is contained within a circle with center \(C\). Points \(A\) and \(B\) lie on the circle. If the area of circle \(C\) is \(25 \pi,\) and the measure of angle \(A C B\) is \(60^{\circ},\) which of the following are possible lengths for side \(A B\) of triangle \(A B C ?\) Indicate all such lengths. a. 3 b. 4 c. 5 d. 6 e. 7

\((a, 6)\) is a point (not shown) in Quadrant I. \((-6, b)\) is a point (not shown) in Quadrant II. $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ a & b \end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

A piece of twine with length of \(t\) is cut into two pieces. The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. Which of the following is the length, in yards, of the longer piece? a. $$\frac{t+3}{3}$$ b. $$\frac{3 t+2}{3}$$ c. $$\frac{t-2}{4}$$ d. $$\frac{3 t+4}{4}$$ e. $$\frac{3 t+2}{4}$$
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