Question

What is the radius of a sphere with a volume of 797 ft^3to the nearest tenth of a
foot?

Answer 1

`\displaystyle r \approx 5.8 \ ft`

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

Volume of a Sphere Formula:
`\displaystyle V = (4)/(3)\pi r^3`

• r is radius

Explanation:

Step 1: Define

Identify variables

Volume V = 797 ft³

Step 2: Solve for r

1. Substitute in variables [Volume of a Sphere Formula]:
   `\displaystyle 797 \ ft^3 = (4)/(3)\pi r^3`
2. [Division Property of Equality] Isolate r term:
   `\displaystyle (2391)/(4 \pi) \ ft^3 =r^3`
3. Rewrite:
   `\displaystyle r^3 = (2391)/(4 \pi) \ ft^3`
4. [Equality Property] Cube root both sides:
   `\displaystyle r = \frac{4782^{(1)/(3)}}{2 \pi^{(1)/(3)}} \ ft`
5. Evaluate:
   `\displaystyle r = 5.75162 \ ft`
6. Round:
   `\displaystyle r \approx 5.8 \ ft`