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

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-AlgebraOrder of Operations: BPEMDASBracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra IEquality PropertiesMultiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityGeometryDiameter Formula:
[tex]\displaystyle d = 2r[/tex]r is radiusVolume Formula [Sphere]:
[tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]r is radiusStep-by-step explanation:Step 1: DefineIdentify given.[tex]\displaystyle d = 26 \ \text{cm}[/tex]Step 2: Find rIn order to find the volume of the sphere, we first need to find the radius:[Diameter Formula] Substitute in variables:
[tex]\displaystyle 26 \ \text{cm} = 2r[/tex][Division Property of Equality] Isolate r:
[tex]\displaystyle r = 13 \ \text{cm}[/tex]∴ we found the radius to be 13 cm.Step 3: Find VolumeNow that we have our radius, we can find the volume of the sphere:[Volume Formula - Sphere] Substitute in variables:
[tex]\displaystyle V = \frac{4}{3}(3.14)(13 \ \text{cm})^3[/tex][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.___Learn more about volume: more about Geometry: : Geometry