Question

Find the diameter of a circle with an area of 256π square meters.

Answer 1

Answer:

d = 32 m

General Formulas and Concepts:

Symbols

• π (pi) ≈ 3.14

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right  

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Geometry

Area of a Circle Formula: A = πr²

• r is radius

Radius Formula: $\displaystyle r = \frac{d}{2}$

• d is diameter

Step-by-step explanation:

Step 1: Define

Identify variables

A = 256π m²

Step 2: Derive

Rewrite formula

1. [Area of a Circle Formula] Substitute in r [Radius Formula]:                          $\displaystyle A = \pi(\frac{d}{2})^2$
2. Evaluate exponents:                                                                                         $\displaystyle A = \pi(\frac{d^2}{4})$
3. Multiply:                                                                                                             $\displaystyle A = \frac{\pi d^2}{4}$

Step 3: Solve for d

1. Substitute in A [Modified Area of a Circle Formula]:                                      $\displaystyle 256 \pi \ m^2 = \frac{\pi d^2}{4}$
2. [Multiplication Property of Equality] Multiply 4 on both sides:                      $\displaystyle 1024 \pi \ m^2 = \pi d^2$
3. [Division Property of Equality] Divide π on both sides:                                  $\displaystyle 1024 \ m^2 = d^2$
4. [Equality Property] Square root both sides:                                                    $\displaystyle 32 \ m = d$
5. Rewrite:                                                                                                             $\displaystyle d = 32 \ m$