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A beverage manufacturer performs a taste-test and discovers the people like their fizzy beverages best when the radius of the bubbles is about 0.5 mm. According to the formula below, what would be the volume of the one of these bubbles?

A beverage manufacturer performs a tastetest and discovers the people like their fizzy beverages best when the radius of the bubbles is about 05 mm According to class=

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Answer with explanation:

Radius of the Bubble = 0.5 mm

Volume of the bubble is given by the formula

[tex]r=[\frac{3V}{4\pi}]^{\frac{1}{3}}[/tex]

Taking cube on both sides

[tex]V=\frac{4\pi\times r^3 }{3}\\\\ V=\frac{4*3.14*(0.5)^3}{3}\\\\V=\frac{12.56\times 0.125}{3}\\\\ V=\frac{1.57}{3}\\\\v=0.52333....[/tex]

Gives,→ V=0.52 mm³(approx)

Option C: about 0.52 mm³

The volume of the sphere will be 0.52 cubic mm. Then the correct option is C.

What is the volume of the sphere?

Let r be the radius of the sphere.

Then the volume of the sphere will be

V = 4/3 πr³ cubic units

The expression is given below.

[tex]\rm r = \sqrt[3]{\dfrac{3V}{4\pi}}[/tex]

Where r is the radius of the sphere and V is the volume of the sphere.

A beverage manufacturer performs a taste test and discovers that people like their fizzy beverages best when the radius of the bubbles is about 0.5 mm.

The expression is solved for V, then the equation will be

[tex]\rm r^3 = \dfrac{3V}{4\pi}\\\\V = \dfrac{4}{3}\pi r^3[/tex]

Then the volume of the sphere will be

V = (4/3) × π × 0.5³

V = 0.52 cubic mm

Thus, the volume of the sphere will be 0.52 cubic mm.

Then the correct option is C.

More about the volume of the sphere link is given below.

https://brainly.com/question/9994313

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