How do you answer this question?

Question

The surface area of a right cylinder is 576(Pi) cm^2. If the radius and height are equal, find the length of the diameter.

Answer 1

Algebra, two equations in two unknowns:
A = 2 pi r*2 + 2 pi r h; r = h; A = 4 pi r*2 = 576 pi.
r^2 = 144; r = 12; d = 24.

Answer 2

The surface area of a right cylinder is 2πrh + 2πr^2, where r = radius and h = height. Both height and radius = x. so the area is

2πx^2 + 2πx^2 = 576π

x^2 = 576/4

x = √144 = 12

x is the same as r, the radius, so the diameter is 2*x = 24

Answer 3

2 pi r h=576 pi
r=h

2 pi r^2=574,6 pi
2r^2=576
r^2=288

r=12.sqr(2)
2r=diameter
=24.sqrt(2)

Answer 4

Let

r = radius
h = height
S = surface area
d = diameter

Given

S = 576π
r = h

Find d.

S = 2πr² + 2πrh = 2πr² + 2πr² = 4πr²
4πr² = 576π
r² = 144
r = 12

d = 2r = 2*12 = 24 cm

Answer 5

A=Π(2r^2+2rh)=576Π
576=2r^2+2r^2=4r^2
r^2=144
r=12 cm
h=12cm
d=24cm