Question

With the given volume of 294 π, what is the radius?
Hight given = 18

Answer 1

`\displaystyle r = 7`

General Formulas and Concepts:

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

Volume of a Cone Formula:
`\displaystyle V = (\pi)/(3) r^2h`

• r is radius
• h is height

Explanation:

Step 1: Define

Identify variables

V = 294π

h = 18

Step 2: Solve for r

1. Substitute in variables [Volume of a Cone Formula]:
   `\displaystyle 294 \pi = (\pi)/(3) r^2(18)`
2. Multiply:
   `\displaystyle 294 \pi = 6 \pi r^2`
3. [Division Property of Equality] Divide 6π on both sides:
   `\displaystyle 49 = r^2`
4. [Equality Property] Square root both sides:
   `\displaystyle 7 = r`
5. Rewrite:
   `\displaystyle r = 7`