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
