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A hemisphere has a diameter of 26 centimeters. What is the volume of a sphere with the same radius? (Use 3.14 for π. Round the answer to the nearest tenth, if necessary. Recall that the formula for the volume of a sphere is v=4/3pir^3.)

A. 2,830.2 cubic centimeters
B. 3,066.0 cubic centimeters
C. 4,599.1 cubic centimeters
D. 9,198.1 cubic centimeters

Respuesta :

Space

Answer:

The volume of the sphere that has the same radius as the given hemisphere is equal to 9198.11 cm³.

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

Algebra I

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Geometry

Diameter Formula:
[tex]\displaystyle d = 2r[/tex]

  • r is radius

Volume Formula [Sphere]:
[tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]

  • r is radius

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle d = 26 \ \text{cm}[/tex]

Step 2: Find r

In order to find the volume of the sphere, we first need to find the radius:

  1. [Diameter Formula] Substitute in variables:
    [tex]\displaystyle 26 \ \text{cm} = 2r[/tex]
  2. [Division Property of Equality] Isolate r:
    [tex]\displaystyle r = 13 \ \text{cm}[/tex]

∴ we found the radius to be 13 cm.

Step 3: Find Volume

Now that we have our radius, we can find the volume of the sphere:

  1. [Volume Formula - Sphere] Substitute in variables:
    [tex]\displaystyle V = \frac{4}{3}(3.14)(13 \ \text{cm})^3[/tex]
  2. [Order of Operations] Evaluate:
    [tex]\displaystyle \begin{aligned}V & = \frac{4}{3}(3.14)(13 \ \text{cm})^3 \\& = \boxed{ 9198.11 \ \text{cm}^3 } \\\end{aligned}[/tex]

∴ the volume of the sphere is equal to 9198.11 cm³.

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Learn more about volume: https://brainly.com/question/27732826

Learn more about Geometry: https://brainly.com/question/27732359

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Topic: Geometry