Answered

Solve the equation [tex]$x = \frac{2}{3} \pi r^3$[/tex] for [tex]$r$[/tex].

A. [tex]$r = \sqrt[3]{3x - 2 \pi}$[/tex]
B. [tex]$r = \sqrt[3]{\frac{2 \pi}{3z}}$[/tex]
C. [tex][tex]$r = \sqrt[3]{\frac{3z}{2 \pi}}$[/tex][/tex]
D. [tex]$r = \sqrt[3]{3x(2 \pi)}$[/tex]



Answer :

GinnyAnswer
To solve the equation [tex]\( x = \frac{2}{3} \pi r^3 \)[/tex] for [tex]\( r \)[/tex], follow these steps:

1. Isolate the term involving [tex]\( r^3 \)[/tex]:

Start with the given equation:
[tex]\[ x = \frac{2}{3} \pi r^3 \][/tex]

To isolate [tex]\( r^3 \)[/tex], multiply both sides of the equation by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[ x \cdot \frac{3}{2} = \pi r^3 \][/tex]

Simplifying the left-hand side:
[tex]\[ \frac{3x}{2} = \pi r^3 \][/tex]

2. Solve for [tex]\( r^3 \)[/tex]:

Next, divide both sides by [tex]\(\pi\)[/tex] to isolate [tex]\( r^3 \)[/tex]:
[tex]\[ \frac{3x}{2\pi} = r^3 \][/tex]

3. Solve for [tex]\( r \)[/tex]:

Finally, take the cube root of both sides of the equation to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt[3]{\frac{3x}{2\pi}} \][/tex]

Thus, the correct solution for [tex]\( r \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[ r = \sqrt[3]{\frac{3x}{2\pi}} \][/tex]

Looking at the given answer choices, this corresponds to option C.

Therefore, the correct answer is:

C. [tex]\( r = \sqrt[3]{\frac{3x}{2\pi}} \)[/tex]

Other Questions