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kogti [31]
3 years ago
13

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

Mathematics
1 answer:
azamat3 years ago
5 0

Answer:

\displaystyle r \approx 5.8 \ ft

General Formulas and Concepts:

<u>Symbols</u>

  • π (pi) ≈ 3.14

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Geometry</u>

Volume of a Sphere Formula: \displaystyle V = \frac{4}{3}\pi r^3

  • <em>r</em> is radius

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

Volume <em>V</em> = 797 ft³

<u>Step 2: Solve for </u><em><u>r</u></em>

  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 <em>r</em> 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
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____________________________________________________________

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