Question

Jesse is filling spherical balloons. When full, one of these balloons has a diameter of 24\text{ cm}24 cm24, start text, space, c, m, end text. Jesse can fill a balloon at a rate of 820\text{ cm}^3820 cm
3

820, start text, space, c, m, end text, cubed per breath.

How many breaths does it take Jesse to fill a balloon?

Answer 1

Answer:

Answer is 8.8

Step-by-step explanation:

8.8 is the answer but Khan academy tells us to round to the nearest whole breathe so the answer is 9.

Answer 2

Answer:

Answer is 8.8

Step-by-step explanation:

The diameter is 24\text{ cm}24 cm24, start text, space, c, m, end text, so the radius is \maroonD{12\text{ cm}}12 cmstart color #ca337c, 12, start text, space, c, m, end text, end color #ca337c.

\begin{aligned} \text{volume}_{\text{sphere}} &= \dfrac{4}{3}\pi (\text{radius length})^3 \\\\ \text{volume}_{\text{full}} &= \dfrac{4}{3}\pi (\maroonD{12})^3\\\\ &\approx \purpleD{7{,}238} \end{aligned}

volume

sphere

​

volume

full

​

​

 

=

3

4

​

π(radius length)

3

=

3

4

​

π(12)

3

≈7,238

​

A fully-inflated balloon has a volume of about \purpleD{7{,}238\text{ cm}^3}7,238 cm

3

start color #7854ab, 7, comma, 238, start text, space, c, m, end text, cubed, end color #7854ab.

Hint #33 / 4

Filling rate

Jesse can fill a balloon at a rate of \goldE{820\text{ cm}^3}820 cm

3

start color #a75a05, 820, start text, space, c, m, end text, cubed, end color #a75a05 per breath.

\begin{aligned} \text{volume}_{\text{filled}} &= (\text{filling rate}) (\text{\# of breaths})\\\\ \purpleD{7{,}238} &\approx \goldE{820} \redE{n}\\\\ \dfrac{\purpleD{7{,}238}}{\goldE{820}} &\approx \redE{n}\\\\ 8.8&\approx \redE{n} \end{aligned}

volume

filled

​

7,238

820

7,238

​

8.8

​

 

=(filling rate)(# of breaths)

≈820n

≈n

≈n

​