i need some help with this?

Question

The radius of a sphere is tripled, by what number is its volume multiplied?

Answer 1

V = (4/3)pi(r^3)

V' = (4/3)pi((3r)^3) = (4/3)pi(27)(r^3)

Answer: 27

Answer 2

The volume of a sphere is given by V = 4/3(pi)r^3
These kinds of problems are what I call, "muddy",
because it can be difficult to figure out what exactly they want. In this case, they want to know the RATIO of the first sphere (which I'll call S(1))to the second, bigger sphere, (S2).

We know V of (S1) = 4/3 (pi) r^2
We are told the radius of (S2) is 3 times that of (S1).
Therefore V of (S2) = 4/3 (pi)(3r)^2, = 4/3 (pi)(9r^2)

I can now compare V(S2) to V(S1)
V(S2)/V(S1) = [4/3 (pi)9r^2]/ [4/3 (pi)r^2]
So V(S2)/V(S1)= 9/1

The volume of the new sphere whose radius was 3 times bigger than the original sphere is 9 times bigger. Its volume was therefore multiplied by 9

I hope this helps. Cheers!

Answer 3

V1 = 4/3 pir1^3
V2 = 4/3 pi (3r1)^3 = 4/3 pi 27r1^3
Thus V2 = 27 V1