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jolli1 [7]
3 years ago
6

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
Mathematics
1 answer:
DanielleElmas [232]3 years ago
8 0
To solve this we are going to use the formula for the volume of a sphere: V= \frac{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= \frac{24}{2} =12. Lets replace that in our formula: 
V= \frac{4}{3} \pi r^3
V= \frac{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= \frac{36}{2} =18. Lets replace that value in our formula one more time:
V= \frac{4}{3} \pi r^3
V= \frac{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 <span>17,194 cm³.</span>
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