Question

What is the approximate diameter of a sphere with a volume of 113 cm^3

Answer 1

Answer:

B. 6 cm

Step-by-step explanation:

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

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 2

Answer:

B. 6 cm

Step-by-step explanation:

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

1. Substitute 113 for "V":

$d=(\frac{6(113)}{\pi }) ^{\frac{1}{3} }$

2. Multiply in the parenthesis:

$d=(\frac{678}{\pi } )^{\frac{1}{3} }$

3. Divide by pi (3.14):

678 ÷ 3.14 = 215.923567

$d=215.9^{\frac{1}{3} }$

4. Apply the exponent:

d = 5.99907...

d = 6 cm

hope this helps!