The radius of the sphere should be about 250.2 centimeters.
Practice makes perfect
We know that one spherical helium-filled balloon with a diameter of 30 centimeters can lift a 14-gram object.
Since the diameter of the balloon is 30 centimeters, the radius of the sphere is r= 302=15 centimeters. Let's find out how much helium is needed to lift a 14-gram object. We will use the formula for the volume of a sphere.
Therefore, we need 4500Ï€ cubic centimeters of helium to lift 14 grams. Let x be the amount of helium that we need to lift a person who weighs 65 kilograms, which is 65 000 grams. Let's write a proportion for the volume of helium and the mass that it can lift.
rcl
65 000 grams & - & x cubic centimeters
14 grams & - & 4500Ï€ cubic centimeters
Now let's write an equation, cross multiply, and solve it for x!
Therefore, we need about 65 636 846.51 cubic centimeters of helium to lift a 65-kilogram person. We are asked to find the size of a balloon that can lift a 65-kilogram person, which will have a volume about 65 636 846.51 cubic centimeters. Let r be its radius.
Let's use the formula for the volume of a sphere to find r. We will round the answer to the nearest tenth.
