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# A cylinder has the SA of 308 cm^2. The height is two times greater than the radius. What is the height of the cylinder?

I'm not sure how to solve this.

SA = 2B + AL (surface area = 2 base areas + lateral area)

Let r = radius, and h = height

308 = 2pi r^2 + 2pi r h = 6pi r^2, since h = 2r

Solve for r,

r = sqrt(308/(6pi))

h = 2r = 8.085 cm <==Answer

The area of a single end = (pi)r^2.  The area of both ends = twice this, or 2(pi)r^2.

The area of the circular surface = 2(pi)rh, or 2(pi)r(2r) or 4(pi)r^2.

Combine both ends and the curved surface, total area = 2(pi)r^2 +  4(pi)r^2.

(A/(6(pi)))^(1/2)  =  r.

(308 cm2/(6(pi)))^(1/2)  = 4.04 cm =  r.  The height is 2x the radius, or 8.08 cm

A cylinder has the SA of 308 cm^2. The height is two times greater than the radius. What is the height of the cylinder?

Volume of cylinder = (area of base)(height)

Volume of cylinder = ((pi)r^2)(height)

Let h = height

then

substitute above into:

Volume of cylinder = ((pi)r^2)(height)

308 = ((3.14)(h/2)^2)(h)

308 = ((3.14)(h^2/4))(h)

308 = (.785h^2)(h)

308 = .785h^3

392.357 = h^3

take cube root of both sides to get:

7.32 cm = h (height)