Question

Would someone please help me?!

1. A sphere has a radius of 4 inches, and a cube-shaped box has an edge length of 7.5 inches. J.D. says the box has a greater volume, so the sphere will fit in the box. Is he correct? Explain.

2. A spherical helium balloon that is 8 feet in diameter can lift about 17 pounds. What does the diameter of a balloon need to be to lift a person who weighs 136 pounds. Explain.

Answer 1

1. Yes. to calculate the volume of a sphere you do
`(4)/(3) \pi r^(3)`, with a radius of 4, you get ≈268.08. then you have to calculate the volume of the cube, which is length x width x height, so you get ≈421.88. 421>268, so JD is correct

2. you need to find out how much weight a balloon with a diameter of one foot can hold, so you divide 8 by 8 to get one, and 17 by eight to get 2.125. You multiply that by 136 to get 289. The balloon would have to be 289 diameters to hold a 136 pound person.

Hope this helps :)