Question

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

Answer 1

Answer:

The value of x is $4\ cm$

Step-by-step explanation:

step 1

Find the radius of the sphere

The surface area of the sphere is equal to

$SA=4\pi r^{2}$

we have

$SA=784\pi\ cm^{2}$

substitute and solve for r

$784\pi=4\pi r^{2}$

Simplify

$r^{2}=196$

square root both sides

$r=14\ cm$

step 2

Find the diameter

Remember that

The diameter is two times the radius

so

$D=2(14)=28\ cm$

step 3

Find the value of x

we have

$D=28\ cm$

$D=4(x+3)\ cm$

equate the equations

$4(x+3)=28$

$(x+3)=7$

$x=7-3=4\ cm$