The volume of Sphere A is the volume of Sphere B when the radius of Sphere B is 2r. Therefore, the volume of Sphere A is:
V(A) = (4/3) * pi * r^3
And the volume of Sphere B is:
V(B) = (4/3) * pi * (2r)^3 = (4/3) * pi * 8r^3 = (32/3) * pi * r^3
To complete the statement "The volume of Sphere A is the volume of Sphere B," we need to set these two volumes equal to each other and solve for r:
(4/3) * pi * r^3 = (32/3) * pi * r^3
r^3 = (32/4) * r^3
r^3 = 8r^3
1 = 8
This equation is not true, so the statement "The volume of Sphere A is the volume of Sphere B" is false.
The volume of Sphere C is times the volume of Sphere A when the radius of Sphere C is 3r. Therefore, the volume of Sphere C is:
V(C) = (4/3) * pi * (3r)^3 = 36 * pi * r^3
To complete the statement "The volume of Sphere C is times the volume of Sphere A," we need to divide the volume of Sphere C by the volume of Sphere A and simplify:
V(C) / V(A) = (36 * pi * r^3) / [(4/3) * pi * r^3] = 27
Therefore, the correct value to complete the statement is 27.