Question

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

Answer 1

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 = (d)/(2)`

• d is diameter

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((d)/(2))^2`
2. Evaluate exponents:
   `\displaystyle A = \pi((d^2)/(4))`
3. Multiply:
   `\displaystyle A = (\pi d^2)/(4)`

Step 3: Solve for d

1. Substitute in A [Modified Area of a Circle Formula]:
   `\displaystyle 256 \pi \ m^2 = (\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`