Question

What is the relationship between the volume and surface area of the sphere shown?

Answer 1

a.V < SA
b.V = SA
c.V > SA

Answer 2

V = 1/3r*(SA)

Answer 3

so the answer is A. V=SA ...Right?

Answer 4

No, for r<3, V<SA; for r=3, V=SA; for r>3, V>SA.

Answer 5

i dont understand you

Answer 6

The question is specifically about this sphere with r = 3, so if
V = 1/3r*(SA) is correct, then
V = SA since V = (1/3)(3)*SA) = SA

Answer 7

so the answer is A

Answer 8

V = SA is choice b, isn't it?

Answer 9

I'm sorry, I thought that the radius was the variable r. Mathstudent is correct for r = 3.

Answer 10

Oh sorry my bad yes i ment B

Answer 11

V = (4/3)(pi)r^3
SA = 4(pi)r^2

For r = 3
V = (4/3)(pi)(3^3) = 4*3^2(pi) = 36(pi)
SA = 4(pi)r^2 = 4(pi)*3^2 = 4*3^2(pi) = 36(pi)
V = SA

Answer 12

Let V be the volume and A be the surface area of the sphere, r be the radius of sphere
V=4/3 pi r^3 ,r^3=3V/4pi, r=(3V/4pi)^1/3
A=4 pi r^2=4pi[(3V/4pi)^1/3 ]^2
A=4pi (3V/4pi)^2/3
A^3=64pi^3 (3V/4pi)^2
A^3=36 pi V^2