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Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{

Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{ cm}2 cm2, space, c, m. He wanted his balloon to be bigger, so he blew 222 big breaths of air into the balloon. Each big breath increased the balloon's radius by 1 \text{ cm}1 cm1, space, c, m. What is the ratio of the current volume of the balloon to the original volume of the balloon?

2 months ago

Solution 1

Guest Guest #9501
2 months ago

The ratio of the current volume of the balloon to the original volume of the balloon is 8.

What is the volume of a sphere?

The volume of a sphere is given by (4\3)πr³ where r is the radius of the sphere.

The initial volume of the balloon = \frac{4}{3} \pi 2^{3}

The initial volume of the balloon =\frac{32}{3} \pi

Radius of the balloon after first breath = 2+1 =3cm

The Radius of the balloon after the second breath = 2+2=4cm

So, the new volume of the balloon = \frac{4}{3} \pi 4^{3}

The new volume of the balloon = \frac{256}{3} \pi

The ratio of new volume to the initial volume = \frac{\frac{256}{3 } \pi }{\frac{32}{3}\pi }

The ratio of new volume to the initial volume =8

Hence, the ratio of the current volume of the balloon to the original volume of the balloon is 8.

To get more about sphere visit:

brainly.com/question/10171109

Solution 2

Guest Guest #9502
2 months ago

Answer:

8 times

Step-by-step explanation:

I found the volume of the sphere. Then increased it how many times he blew. That was the ratio.

Also, Khan :)

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