Respuesta :

themathexpertise

Answer:

B. 6 cm

Step-by-step explanation:

[tex]\text{Take the volume of a sphere and solve for r.}\\V=\frac{4}{3}\pi r^3\\\text{We already know that the volume is 113, so substitute that value.}\\113=\frac{4}{3}\pi r^3\\\text{Divide both sides by 4/3 pi.}\\\frac{113}{\frac{4}{3}\pi}=r^3\\\text{Divide 113 by 4/3 pi.}\\r^3=26.98\\\text{For a more accessible value, round up.}\\r^3 \approx27\\\text{Take the cube root of both sides.}\\r=3[/tex]

Now that the radius is known, all we have to do is multiply it by 2 to get the diameter. Here the answer is simply 3 * 2, or 6.

Answer:

B. 6 cm

Step-by-step explanation:

You can use the formulas [tex]d=(\frac{6V}{\pi } )^{\frac{1}{3} }[/tex] or [tex]d = \sqrt[3]{\frac{6V}{\pi } }[/tex] to solve for diameter using volume. I will use the first forumla for this problem.

1. Substitute 113 for "V":

[tex]d=(\frac{6(113)}{\pi }) ^{\frac{1}{3} }[/tex]

2. Multiply in the parenthesis:

[tex]d=(\frac{678}{\pi } )^{\frac{1}{3} }[/tex]

3. Divide by pi (3.14):

678 ÷ 3.14 = 215.923567

[tex]d=215.9^{\frac{1}{3} }[/tex]

4. Apply the exponent:

d = 5.99907...

d = 6 cm

hope this helps!

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