Your classmate claims that if you
double the radius of a sphere, its surface area and
volume will quadruple. what is your classmate’s
error? explain.

SA of a sphere is 4πr²   Using a sample of radius 3 the SA would be 36π²
(4πx3²)   If we double the radius and make it 6, the SA would be 144π²
So for Surface area, your classmate is correct.

What about the volume?  V of a Sphere = 4/3 π r³
Again using 3 the Volume of a Sphere with radius 3 = 4/3 π 27
But the volume of a sphere with radius 6 = 4/3 π 216 which is eight times the volume of the smaller sphere. (27 x 8 =216)  So your friend is right about Surface Area but wrong about the volume.