Question

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

Answer 1

B. 6 cm

Explanation:

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

1. Substitute 113 for "V":

`d=((6(113))/(\pi )) ^{(1)/(3) }`

2. Multiply in the parenthesis:

`d=((678)/(\pi ) )^{(1)/(3) }`

3. Divide by pi (3.14):

678 ÷ 3.14 = 215.923567

`d=215.9^{(1)/(3) }`

4. Apply the exponent:

d = 5.99907...

d = 6 cm

hope this helps!

Answer 2

B. 6 cm

Explanation:

`\text{Take the volume of a sphere and solve for r.}\\V=(4)/(3)\pi r^3\\\text{We already know that the volume is 113, so substitute that value.}\\113=(4)/(3)\pi r^3\\\text{Divide both sides by 4/3 pi.}\\(113)/((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.