In the case of the prism, you doubled three dimensions. In the

case of the sphere, you doubled just the radius. Why do you

get the same results?

We obtain the same result since it increases in the same proportion

Step-by-step explanation:

TWe have that the formula of the volume the prism is:

Vp = a * b * c

And in the case of the sphere, it is:

Vs = 4/3 * pi * r ^ 3

In the first they tell us that each dimension is doubled:

Vp = 2a * 2b * 2c

Vp = 2 (^ 3) * a * b * c

Vp = 8 * a * b * c

That is, the volume of the prism increases by 8 times compared to the previous one.

Now the sphere, the radius is doubled:

Vs = 4/3 * pi * (2r) ^ 3

Vs = 4/3 * pi * 2 ^ 3 * r ^ 3

Vs = 8 * [4/3 * pi * r ^ 3]

Which means, that for the sphere, it also increased 8 times.