Answer:
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.
