/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 16 Find the area of the circle with... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 16

Find the area of the circle with the given radius or diameter. $$d=1256 \mathrm{ft}$$

Short Answer

Expert verified
The area of the circle is approximately 1,239,446.81 square feet.

Step by step solution

01

Determine if Diameter or Radius

The problem provides the diameter of the circle, which is 1256 ft. We need the radius to find the area.
02

Calculate the Radius

The radius is half of the diameter. Therefore, the radius is calculated as follows: \[ r = \frac{d}{2} = \frac{1256}{2} = 628 \text{ ft} \]
03

Use the Area Formula

To find the area of a circle, use the formula: \[ A = \pi r^2 \].With \( r = 628 \text{ ft} \), we substitute into the formula to get:\[ A = \pi (628)^2 \].
04

Calculate the Area

Perform the calculations using the value of \( pi \) (approximately 3.14159):\[ A = 3.14159 \times (628)^2 \]\[ A \approx 3.14159 \times 394,384 \]\[ A \approx 1,239,446.8096 \text{ square feet} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Diameter
In the world of circles, the diameter is a crucial measurement. It refers to the longest distance across the circle, passing directly through the center. Think of it as slicing the circle down its middle, from one edge to the opposite edge. This length is called the diameter, and it is usually denoted by the letter "d."

Here's why diameter is important:
  • It helps in easily understanding the size of a circle.
  • Knowing the diameter allows us to find the radius, which is essential for many calculations involving circles.
In most exercises, you might be given the diameter, and you can always find the radius from it. To do so, simply remember that the diameter is twice the radius. This leads us perfectly into the next concept鈥攖he radius.
Exploring the Radius
The radius is another fundamental feature of a circle, and it signifies half the length of the diameter. The radius extends from the center of the circle to any point on its circumference. It's essentially a building block for numerous circle-related formulas.

Given the diameter, calculating the radius is quite straightforward. You can use the simple formula: \[ r = \frac{d}{2} \] where "r" stands for the radius and "d" represents the diameter.

Knowing the radius is vital for many calculations, especially when finding areas, circumferences, or even working with sectors of circles. By understanding the radius, you unlock the potential to explore the circle more fully.
The Circle Area Formula
Once you have the radius at hand, determining the area of a circle is simple with the help of the circle area formula: \[ A = \pi r^2 \] where:
  • "A" denotes the area.
  • "r" refers to the radius.
  • "\pi" (pi) is a constant, approximately equal to 3.14159.
This formula is derived from the relationship between the radius and the total space enclosed within the circle. By squaring the radius and multiplying it by \( \pi \), you calculate the number of square units needed to cover the circle's interior.

Thus, the concept of area using this formula shows how closely linked the radius and area of a circle are. With just the radius and the universal constant pi, you can determine how large or small any circle is.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve the given problems. A transmitting tower is supported by a wire that makes an angle of \(52^{\circ}\) with the level ground. What is the angle between the tower and the wire?

Solve the given problems. A walkway 3.0 m wide is constructed along the outside edge of a square courtyard. If the perimeter of the courtyard is \(320 \mathrm{m}\) (a) what is the perimeter of the square formed by the outer edge of the walkway? (b) What is the area of the walkway?

Solve the given problems. The circumference of a basketball is about 29.8 in. What is its volume?

Solve the given problems. The CN Tower in Toronto has an observation deck at \(346 \mathrm{m}\) above the ground. Assuming ground level and Lake Ontario level are equal, how far can a person see from the deck? (The radius of Earth is 6378 km.)

Solve the given problems. The Alaskan oil pipeline is 750 mi long and has a diameter of \(4.0 \mathrm{ft}\). What is the maximum volume of the pipeline?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.