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

The value of x is
`4\ cm`

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`