A design on a balloon is 6 cm wide when the balloon holds 44 cm to the third power of air. How much must

the balloon hold for the design to be 24 cm wide?

Since the "width" increases by a factor of 4, the volume will increase by a factor of 4^3 = 64, even if the balloon is not spherical. The only requirement is that the shape remain the same, which is a reasonable assumption. The balloon you are talking about is not spherical; if it were, the original volume would be 113.1 cm^3.

So the answer is 64 x 44 = ___ cm^3.

thank you

2816 cm^3

To find the volume of air that the balloon must hold for the design to be 24 cm wide, we can use the concept that the volume will increase by a factor of 4 raised to the power of 3.

1. Start by calculating the volume increase factor:
Factor = (New width / Original width) ^ 3

In this case, the new width is 24 cm and the original width is 6 cm:
Factor = (24 / 6) ^ 3
= 4 ^ 3
= 64

2. Next, multiply the volume of air the original balloon holds by the volume increase factor:
New volume = Original volume x Factor

The original volume is given as 44 cm^3:
New volume = 44 cm^3 x 64
= 2816 cm^3

Therefore, the balloon must hold 2816 cm^3 of air for the design to be 24 cm wide.