What is the approximate diameter of a sphere with a volume of 34 cm3?

4 centimeters

Step-by-step explanation:

The volume of a sphere can be found using the following formula:

v=4/3*π*r^3

We know the volume is 34 cm^3. Therefore, we can substitute 34 in for v.

34=4/3*π*r^3

We are trying to find r, or the radius. Therefore, we need to get r by itself on one side of the equation.

First, divide both sides by pi.

34/π=4/3*π*r^3 /π

34/π =4/3 * r^3

10.8225361= 4/3 * r^3

Next, divide both sides by 4/3, or multiply by the reciprocal of the fraction.

To find the reciprocal, flip the numerator and denominator of the fraction

4/3 ---flip top number and bottom number --> 3/4

3/4 * 10.8225361= 4/3*r^3 *3/4

3/4* 10.8225361= r^3

8.11690208= r^3

Finally, take the cube root of both sides of the equation.

∛8.11690208=∛r^3

∛8.11690208=r

2.00969477=r

Round to the nearest whole number.

r=2

Now, we must find the diameter. The diameter is twice the radius.

d=2r

The radius is 2 cm.

d= 2 * 2cm

d= 4 cm

The diameter is 4 cm

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step-by-step explanation: