Question

Jake volunteers to help out his younger brother's basketball team in his free time. One of those tasks is to ensure that all the basketballs have enough air in them. Given that a properly inflated basketball measures 8.8 inches across, what is the total volume of air inside one-sixth of Jake's basketball? Assume the shape is spherical.

Answer 1

To find the total volume of air inside one-sixth of Jake's basketball, we use the formula for the volume of a sphere. The radius of the basketball is found by converting the diameter to centimeters. The total volume is then divided by 6 to find the volume of one-sixth of the basketball.

Step-by-step explanation:

To find the total volume of air inside one-sixth of Jake's basketball, we first need to find the radius of the basketball. The basketball has a diameter of 8.8 inches, so its radius is half of that, which is 4.4 inches. To convert inches to centimeters, multiply the inches by 2.54. So, the radius of the basketball is approximately 11.18 cm.

We know that the volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius. Plugging in the values, we get V = (4/3)π * (11.18 cm)^3. Simplifying this, we get V ≈ 7,959.42 cm^3.

Since we want to find the volume of one-sixth of the basketball, we divide the total volume by 6. So, the total volume of air inside one-sixth of Jake's basketball is approximately 1,326.57 cm^3.

Answer 2

The total volume of air inside one-sixth of Jake's basketball is 19.36 cubic inches.

Step-by-step explanation:

The volume of air inside one-sixth of Jake's basketball can be calculated by finding the volume of a sphere with a radius equal to one-sixth the radius of the basketball.

The radius of the basketball is 8.8 inches, so the radius of one-sixth of the basketball is (1/6) * 8.8 = 1.47 inches.

Using the formula for the volume of a sphere (V = (4/3) * π * r^3), we can calculate the volume of one-sixth of the basketball:

V = (4/3) * π * (1.47 inches)^3 = 19.36 cubic inches.

Therefore, the total volume of air inside one-sixth of Jake's basketball is 19.36 cubic inches.