how do I find the height of a sphere when I have a surface area of 800cm2?
The height of a sphere would be its diameter. Let's call this " d " .
And the formula for the surface area of a sphere is...
surface area = 4 * pi * (radius)2
Since radius = d/2 , we can say...
surface area = 4 * pi * (d / 2)2
The problem tells us that surface area = 800 cm2
800 cm2 = 4 * pi * (d / 2)2
Multiply out the exponent.
800 cm2 = 4 * pi * d2 / 4
800 cm2 = pi * d2
Divide both sides by pi .
800 / pi cm2 = d2
Take the positive square root of both sides.
√[ 800 / pi ] cm = d
15.958 cm ≈ d