Question

Last autumn, julia noticed something interesting as she blew up spherical balloons for harris's birthday party. she calculated the volume of a balloon with a radius of 4 cm and then the volume of a balloon with a radius of 8cm. did she discover that the volume is twice as big when the radius is doubled?

Answer 1

She would not find out that the volume is twice as big when the radius is doubled.

Answer 2

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:
$\frac{4}{3} \pi \: {r}^{3}$
Let's take 丌 as 3.14

The volume of the balloon with 4cm radius:
$\frac{4}{3}(3.14) \times {4}^{3} \\ = 4.18667 \times 64 \\ = 267.94688$

The volume of the balloon with 8cm radius:
$\frac{4}{3}(3.14) \times {8}^{3} \\ = 4.18667 \times 512 \\ = 2143.57504$
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!