Question

Sphere a has a radius of r feet. sphere b has a radius of 2r feet. sphere c has a radius of 3r feet. write the appropriate values to complete the statements.

The volume of Sphere A is __ the volume of Sphere B.
The volume of Sphere C is __ times the volume of Sphere A.

1/27 1/9 1/8 1/4 2 8 9 27

Answer 1

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.

Answer 2

Answer: 3r

Step-by-step explanation: because 2r+1r=3r