Help with Open ended problem?

[abdel]

A physical education teacher was getting ready for gym class one day . he measured the circumference of the basketball to be 9 inches when it is filled with air . he then went on to pose the following question to his classes : use 3.14

A ) How much material is needed to make four baskeballs?

b ) How much air will the four balls hold combined ?

c) If the basketballs are stored four to a box in cubic boxes whose edges are 15 inches long, what percent of the box is not filled by the balls?

d.) The school would like to save money and storage space by buying smaller boxes to store the balls. What is the smallest size for the box where it will still hold four balls and each edge will be a whole number?

If someone could help explain it'd be much appreciated thanks.

 

[HallsofIvy]

A physical education teacher was getting ready for gym class one day . he measured the circumference of the basketball to be 9 inches when it is filled with air . he then went on to pose the following question to his classes : use 3.14

A ) How much material is needed to make four baskeballs?

Who ever asked this question expects you to know the formulas for circumference of a circle, in terms of its radius, so that you can use "the circumference of the basketball to be 9 inches" to find the radius of the ball, and the formula for the surface area of a sphere, in terms of its radius.

b ) How much air will the four balls hold combined ?

Use the radius, from (A), and the formula for volume of a sphere, in terms of its radius, to find the volume of one ball, then, of course, multiply by 4.

c) If the basketballs are stored four to a box in cubic boxes whose edges are 15 inches long, what percent of the box is not filled by the balls?

In (b), you found the volume that the four balls will take up. Find the volume of a cube with sides of length 15 inches, and subtract.

d.) The school would like to save money and storage space by buying smaller boxes to store the balls. What is the smallest size for the box where it will still hold four balls and each edge will be a whole number?

You have already found the radii of the balls so you can find the diameter. If you put four balls in a single layer, you can fit them in a box where the length and width are two diameters and the height is one diameter.

If someone could help explain it'd be much appreciated thanks.