A sphere has a diameter of 4(x+3) centimeters and a surface area of 784Ο€ square centimeters. Find the value of x.

Accepted Solution

Answer:The value of x is [tex]4\ cm[/tex]Step-by-step explanation:step 1Find the radius of the sphereThe surface area of the sphere is equal to[tex]SA=4\pi r^{2}[/tex]we have[tex]SA=784\pi\ cm^{2}[/tex]substitute and solve for r[tex]784\pi=4\pi r^{2}[/tex]Simplify[tex]r^{2}=196[/tex]square root both sides[tex]r=14\ cm[/tex]step 2Find the diameterRemember thatThe diameter is two times the radiusso[tex]D=2(14)=28\ cm[/tex]step 3Find the value of xwe have[tex]D=28\ cm[/tex][tex]D=4(x+3)\ cm[/tex]equate the equations[tex]4(x+3)=28[/tex][tex](x+3)=7[/tex][tex]x=7-3=4\ cm[/tex]