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Chapter 1: Problem 8

Find the circumference of a circle with a diameter of \(13 \mathrm{~cm}\).

Short Answer

Expert verified
The circumference is approximately 40.84 cm.

Step by step solution

01

- Understand the formula

To find the circumference of a circle, use the formula: \[ C = \pi \times d \] where \( C \) is the circumference and \( d \) is the diameter of the circle.
02

- Identify the given values

From the problem, the diameter \( d \) of the circle is given as \( 13 \mathrm{~cm} \).
03

- Substitute the values into the formula

Replace \( d \) with \( 13 \mathrm{~cm} \) in the formula: \[ C = \pi \times 13 \mathrm{~cm} \]
04

- Calculate the circumference

Calculate the product to find the circumference: \[ C = \pi \times 13 \mathrm{~cm} \approx 40.84 \mathrm{~cm} \] (Note: The value of \pi \ is approximately 3.14)

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Key Concepts

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

Geometry
Geometry is a branch of mathematics that studies shapes, sizes, and properties of figures. It includes concepts like points, lines, planes, angles, and surfaces. One important shape in geometry is the circle. Understanding geometric principles helps solve problems related to measurement and dimensions. By learning about the properties of circles, you can easily find measurements like the circumference, diameter, and area.
Circle Calculations
To calculate various measurements of a circle, you need to know certain key formulas. The main components of a circle include the diameter, radius, and circumference.
The diameter is the distance across the circle, passing through the center. The radius is half of the diameter and extends from the center to the edge of the circle. The circumference is the total distance around the circle.
To find the circumference, you can use the formula:

  • For circles where the diameter (\( d\) is known: \[ C = \pi \times d\]
  • For circles where the radius (\( r \)) is known:\[ C = 2 \pi \times r\]
Knowing these formulas makes it easy to switch between different measurements and solve various circle-related problems.
Mathematical Formulas
Mathematical formulas are essential tools that help solve problems quickly and accurately. To find the circumference of a circle, you need to know the formula \(C = \pi \times d\) where \( C \) is the circumference and \(d\) is the diameter.

By substituting the given diameter (13 cm) into the formula, you get:

\(C = \pi \times 13 \approx 40.84 \mathrm{cm}\).
Using the approximate value of \(\pi\) (3.14) simplifies calculations and provides a practical way to determine the circumference.

Practicing these formulas builds a strong foundation for more complex mathematical concepts and improves problem-solving skills.

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