How to find the diameter of a sphere

The formula for the volume of a sphere is:

To figure out how far the sphere rolled, we need to know the circumference, so we must first figure out radius. Solve the formula for volume in terms of radius:

Since the answer asks us to round to the nearest integer, we are safe to round to at this point.

To find circumference, we now apply our circumference formula:

If our boulder rolled times, it covered that many times its own circumference.

Thus, our boulder rolled for

1. Use the volume to find the radius:

2. Use the radius to find the diameter:

To answer this question, we must calculate the volume of the ball using the equation for the volume of a sphere. The equation for the volume of a sphere is four-thirds multiplied by pi, which is then multiplied by the radius cubed. The equation can be written like this:

We are given the diameter of the sphere in the problem, which is . To get the radius from the diameter, we divide the diameter by . So, for this data:

We can then plug our newly found radius of two into the equation to find the volume. For this data:

We then multiply by .

We finally substitute 3.14 for pi and multiply again to get our answer.

The question asked us to round to the nearest whole cubic inch. To do this, we round a number up one place if the last digit is a 5, 6, 7, 8, or 9, and we round it down if the last digit is a 1, 2, 3, or 4. Therefore:

Therefore our answer is .

To solve, simply remember that diameter is twice the radius. Don't be fooled when the radius is an algebraic expression and incorporates the arbitrary constant . Thus,

This question relies on knowledge of the formula for volume of a sphere, which is as follows:

In this equation, we have two variables, and . Additionally, we know that and is unknown. You can begin by rearranging the volume equation so it is solved for , then plug in and solve for :

Rearranged form:

Plug in for V

Simplify the part under the cubed root

1. Cancel the 's since they are in the numerator and denominator.

2. Simplify the fraction and the :

Thus we are left with

Then, either use your calculator and enter Or recall that in order to find that .

We're almost there, but we need to go a step further. Dodge the trap answer "" and carry on. Read the question carefully to see that we need the diameter, not the radius.

So

is our final answer.