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. HI
NT! 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.
Question 1 options:
The formula for the surface area of a sphere is 4 x pi x radius^2
The formula for the volume of a sphere is 4/3 x pi x radius^3.
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
examples 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
