The surface of a sphere can be determined using the formula

The surface of a sphere can be determined using the formula s = 4 pie r where s is the surface area (measured is square inches) of the sphere and r is the radius of the sphere (measured is inches). Suppose the diameter of the sphere is 14 inches. Determine the surface area of that sphere (measured in square inches Write a formula that relates the surface are of the diameter, d, of the sphere Suppose the surface area of the sphere 40 square inches. Determine the radius of the sphere (measured in inches) Write a formula that determine the radius of the sphere gives the surface area of the sphere S.

Solution

given

Surface Area of a Sphere(S) = 4 pi r ²

^{here r is radius}

^{S =} 4 pi r ²

^{given diameter of the sphere = 14 inches}

^{so diameter = 2radius}

        ^{14 =2radius}

^{radius = 7}

^S= 4 pi 7 ²

^{S = 4 pi 49}

^{S= 196 pi}

^2).

^{we konw that} diameter = 2radius

let us say d = diameter

so Surface Area of a Sphere(S) = 4 pi r ²

S = pi (2r) ²

S = pi d ²

^{3) given S= 42}

^{so 42 =}4 pi r ²

21 =2pi r ²  

pi =3.14

21 = 2x3.14 r^2

r^2 = 21/6.28

r^2 =3.344

r = 1.83

4).

Surface Area of a Sphere(S) = 4 pi r ²

S= 4 pi r ²

r ² = S/4pi

r = sqrt [ S / 4pi ]