Question

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?

Answer 1

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

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.