What size does the radius of a sphere need to be for its volume to be larger than its surface area? hint! it is less than 10. hint! it is not a whole number. if you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume. to get full points you will need to show me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.

We know that
volume of a sphere=(4/3)*pi*r³> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²

so
the volume of a sphere=(r/3)*surface area of sphere
therefore

if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere

if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere

if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere

example
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³> 113.04 unit³
surface area=4*pi*3²> 113.04 units²
volume is equal to surface area

2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³> 4186.67 unit³
surface area=4*pi*10²> 1256 units²
volume is > surface area

3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³> 33.49 unit³
surface area=4*pi*2²> 50.24 units²
volume is <  surface area

The answer is 8 apex