Mathematics, 20.05.2020 02:57 Marliii363782

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

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Answer from: jada6292

d = 32 m

General Formulas and Concepts:

Symbols

π (pi) ≈ 3.14

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition 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

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

Step 3: Solve for d

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

Answer from: Quest

Arhombus is a quadrilateral.

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step-by-step explanation:

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