Problema Solution
If a sphere has a diameter of 4 units, which is numerically greater, its surface area or its volume? What if the diameter is 6 units?
Answer provided by our tutors
IF DIAMETER IS 4 UNITS
Volume, V = (4/3)*Pi*r^3
Surface Area, S = 4*Pi*r^2
r = 2
So, V = (4/3)*Pi*2^3 = 33.51
and S = 4*Pi*2^2 = 50.26
Surface area is numerically greater for r = 2
IF DIAMETER IS 6 UNITS
Volume, V = (4/3)*Pi*r^3
Surface Area, S = 4*Pi*r^2
r = 3
So, V = (4/3)*Pi*3^3 = 113.10
and S = 4*Pi*2^3 = 113.10
Surface area is numerically equal to volume when r = 6