Question

What is the volume of a sphere with a radius of 6 units

Answer 1

`288\pi`
It equals 904.78 all together. if you were to take 904.78 and divide it by 3.14 you'd get 288

Answer 2

The correct answer is: [B]: " 288
`\pi` units³ " .

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Step-by-step explanation:

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The formula for the volume, "V" , of a sphere is:

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→ V =
`(4)/(3)  *  \pi  *  r^(3)` ;

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in which:

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V = volume (in "units³ " ; or, write as "cubic units" ).

in our case, we our not given specific units; but simply "units" ;

as such, the volume is expressed as: "units³ " ; or "cubic units".

Note: When calculating the volume of a solid:

I f not given ANY type of units — {or even given the word "units" / for the type of units / as in this particular question/problem} — as the type of units ;

→ then, we express the "volume" of a solid — in:

"cubic units" ; or, " units³ " .

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So: The volume, "V" ; for a "sphere" ; can be calculated using the formula:

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→ V =
`(4)/(3)  *  \pi  *  r^(3)` ;

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in which:

→ V = volume {of the "sphere" ; in: ["units³ "] ; as aforementioned;

→
`\pi` ≈ 3.14 ;

{ Note: For our purposes, we shall use the number; " 3.14 " ; as an approximation for "
`\pi` " .}.

→ r = "radius" = " 6 units " ; ← (given) ;

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So, let us plug in these values into the formula;

→ to solve for the volume, "V" ; of the sphere:

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→ V =
`(4)/(3)` *
`\pi` * r³ ;

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→ V =
`(4)/(3) * [tex]\pi` * (6 units)³ ;

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Note: (6 units)³ = 6³ * (units)³ ;

→ {since: " (ab)ⁿ = aⁿ bⁿ ".}. .

→ 6³ * (units)³ = ?? " ;

= 6³ = 6 * 6 * 6 = 36 * 6 = 216 .

(or: Use calculator: " 6³ = 216 " .).

→ 6³ * (units)³ = 216 units³ .

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So: V =
`(4)/(3)` * 3.14 * (216 units³) = _?_ units³ ?? ;

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→ V = [
`((4)/(3)) * (3.14) * (216)` ] units³ ;

= 904.3200000000000072 units³ . (used calculator).

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Now, upon examining the 4 (four) answer choices provided, we notice that "none" of them give this very [directly aforementioned] answer.

Furthermore, upon examining examining the 4 (four) answer choices provided, we notice that EACH answer choice does, in fact, list an answer with units of: " units³ " .

However, note that for EACH of the 4 (four) answer choices provided, we notice that ALL of the "answer choices" provided; for the "volume" of the "sphere" are given in terms of: "
`\pi` " .

So, if we take our calculated answer for the "volume" of the "sphere", which, as aforementioned, is:

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→ V = " 904.3200000000000072 units³ " .

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→ AND: We divide that numeric value by "
`\pi`" ;

→ {that is: divide that numeric value by the approximation

for: "
`\pi` " ;

→ that is; divide that numeric value by: " 3.14 " ;

→ We can find a "coefficient" of sorts, to:

"
`\pi` " ;

→ when "
`\pi` " ; is written as a symbol .

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If this number is very close to one of the 4 (four) answer choices provided;

→ that is, close to the "coefficient" of: "
`\pi` " ;

→ when "
`\pi` " ; is written as a symbol ;

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→ Then this should reflect the correct answer choice.

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Now, let us calculate; as follows:

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→ " 904.3200000000000072 " ;

÷ " 3.14 "

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to get:

= " 288.000000000000002293 " ;

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→ which corresponds to:

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→ Answer choice: [B]: " 288
`\pi` units³ " .

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Source used: "Web 2.0 scientific calculator." Online Scientific Calculator. 2018. Web. Date accessed/used: 14 Nov 2018 .

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