The volume enclosed by a sphere is given by the formula:

where  is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be meters. Now we can get:

The volume of a sphere is:

Where is the radius of the sphere. We know the volume and can solve the formula for :

 inches

So we can get:

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

 centimeters

 centimeters

Use the volume formula, substituting :

 cubic centimeters

The volume of the cube is  cubic centimeters. Multiply by the number of grams per cubic centimeter to get  grams, or  kilograms.

Divide each dimension in inches by 12 to convert from inches to feet:

 feet

 feet

 feet

Multiply the three to get the volume:

 cubic feet

Use the volume formula, substituting  :

Volume of Cube = side³ = (4”)³ = 64 in³

Volume of Sphere = (4/3) * π * r³ = (4/3) * π * 1³ = (4/3) * π * 1³ = (4/3) * π = 4.187 in³

Difference = Volume of Cube – Volume of Sphere = 64 – 4.187 = 59.813 in³

The formula for the volume of a sphere is 4πr³/3. Because this formula is in terms of the radius, it would be easier for us to determine how the change in the radius affects the volume. Since we are told the diameter is doubled, we need to first determine how the change in the diameter affects the change in radius.

Let us call the sphere's original diameter d and its original radius r. We know that d = 2r.

Let's call the final diameter of the sphere D. Because the diameter is doubled, we know that D = 2d. We can substitute the value of d and obtain D = 2(2r) = 4r.

Let's call the final radius of the sphere R. We know that D = 2R, so we can now substituate this into the previous equation and write 2R = 4r. If we simplify this, we see that R = 2r. This means that the final radius is twice as large as the initial radius.

The initial volume of the sphere is 4πr³/3. The final volume of the sphere is 4πR³/3. Because R = 2r, we can substitute the value of R to obtain 4π(2r)³/3. When we simplify this, we get 4π(8r³)/3 = 32πr³/3.

In order to determine the factor by which the volume has increased, we need to find the ratio of the final volume to the initial volume.

32πr³/3 divided by 4πr³/3 = 8

The volume has increased by a factor of 8. 

Volume of a sphere is 4Πr³/3. Setting that equation equal to the original volume, the new volume is given as 8*4Πr³/3, which can be rewritten as 4Π8r³/3, and can be added to the radius value by 4Π(2r)³/3 since 8 si the cube of 2. This means the radius goes up by a factor of 2

Careful not to mix up radius and diameter. First, we need to identify that the second ball has a radius that is 4 times as large as the first ball.  The radius of the first ball is (1/2)x and the radius of the second ball is 2x. The volume of the second ball will be 4³, or 64 times bigger than the first ball.  So the second ball has a volume of 2 * 64 = 128.