Can you solve the equation A = 2(pi)r^2 2(pi)rh?

Question

can you solve the equation A = 2(pi)r^2 2(pi)rh ?

Answer 1

Solve for what variable?

pi=approx. 3.14

r=radius

h=height

SA=2(pi)r^2+2(pi)rh

Factor by taking 2(pi)r common.

SA=2pi*r(r+h)

Recall that 2pi*r=Circumference=C, thus,

SA=C(r+h)

Solve for h.

SA=C(r+h)

SA/C=r+h

SA/C -r=h

or with a common denominator:

(SA-Cr)/C=h

C=2pi*r, Cr=2pi*r*r=2pi*r^2=2A

(SA-2A)/C=h

Or only with r,

(SA-2pi*R^2)/(2pi*r)=h

Solve for C:

SA=C(r+h)

SA/(r+h)=C

Solve for r:

For this we enter the quadratic ax^2+bx+c=0.

SA=2pi*r^2+2pi*rh

2pi*r^2+2pi*h*r=SA

Divide by 2pi throughout.

r^2+hr=SA/2pi

Replace h with 2x, where h=2x so x is half the height.

r^2+2xr=SA/2pi

to complete the square add x^2.

r^2+2xr+x^2=SA/2pi+x^2

(r+x)^2=(SA+2pi*x^2)/2pi

Given:

SA>0

x>0

r>0

b/c they are all measurements,

r+x=+/-sqrt(SA+2pi*x^2)/sqrt2pi

r=-x+/-sqrt(SA+2pi*x^2)/sqrt2pi

Only the positive solution will be taken because r>0.

Thus,

-x+/-sqrt(SA+2pi*x^2)/sqrt2pi>0

-x+/-sqrt(SA+2pi*x^2)>0

x<+/-sqrt(SA+2pi*x^2)

IF:

x<sqrt(SA+2pi*x^2)

Then take the positive square root.

IF:

x>sqrt(SA+2pi*x^2)

Then take the negative square root.

Hope this helped. Peace

Answer 2

Yes it does look like the equation for calculating the volume of a cylinder that has

radius = r

height = h

π = 3.14159

volume = A

The equation is missing a + sign between the 2 and 2.

A = 2*π*r² + 2*π*h

You ask to solve the equation. In the current state, it is solved for A, the volume.

To solve for h, the height

A = 2*π*r² + 2*π*h

A - 2*π*r² = 2*π*h

h = (A - 2*π*r²) / (2*π)

To solve it for r, the radius

A = 2*π*r² + 2*π*h

2*π*r² = A - 2*π*h

r² = (A - 2*π*h) / (2*π)

......._______________

r = √(A - 2*π*h) / (2*π)

Answer 3

the area of a cylinder

peace...