Question

A spherical balloon was inflated such that it had a diameter of 24 centimeters. Additional helium was then added to the balloon until it had a diameter of 36 centimeters. Approximately what volume of additional helium was added to the balloon? 904 cm³ 7235 cm³ 17,194 cm³ 24,429 cm³

Answer 1

17,190

Explanation:

i took the test and it's right.

Answer 2

To solve this we are going to use the formula for the volume of a sphere:
`V= (4)/(3) \pi r^3`
where

`r` is the radius of the sphere

Remember that the radius of a sphere is half its diameter; since the first radius of our sphere is 24 cm,
`r= (24)/(2) =12`. Lets replace that in our formula:

`V= (4)/(3) \pi r^3`

`V= (4)/(3) \pi (12)^3`

`V=7238.23 cm^3`

Now, the second diameter of our sphere is 36, so its radius will be:
`r= (36)/(2) =18`. Lets replace that value in our formula one more time:

`V= (4)/(3) \pi r^3`

`V= (4)/(3) \pi (18)^3`

`V=24429.02`

To find the volume of the additional helium, we are going to subtract the volumes:
Volume of helium=
`24429.02cm^3-7238.23cm^3=17190.79cm^3`

We can conclude that the volume of additional helium in the balloon is approximately 17,194 cm³.