To find whether the volume would be doubled when the radius is,we can find the volume of the two balloons.
The formula of a sphere is:
[tex] \frac{4}{3} \pi \: {r}^{3} [/tex]
Let's take 丌 as 3.14
The volume of the balloon with 4cm radius:
[tex] \frac{4}{3}(3.14) \times {4}^{3} \\ = 4.18667 \times 64 \\ = 267.94688[/tex]
The volume of the balloon with 8cm radius:
[tex] \frac{4}{3}(3.14) \times {8}^{3} \\ = 4.18667 \times 512 \\ = 2143.57504[/tex]
As we can see,
267.94668 × 2 = 535.89 ≠2145.56
Thus,she wouldn't discover that the volume is twice as big when the radius is doubled.
Hope it helps!
