Question

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

Answer 1

Answer:

$\displaystyle r \approx 5.8 \ ft$

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: $\displaystyle V = \frac{4}{3}\pi r^3$

• r is radius

Step-by-step explanation:

Step 1: Define

Identify variables

Volume V = 797 ft³

Step 2: Solve for r

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