In order to solve problems which require application of the

volume and

surface area for cylinders, it is necessary to

Volume: V = pr^{2}h

Surface Area: S = 2pr^{2} + 2prh

Notice that these factored versions of the

surface area formula are sometimes easier to use:

S = 2pr^{2} + 2prh = 2p(r^{2} + rh) = 2pr(r + h)

To get started, we need to organize as much of the given information as possible into a known formula. Since the

volume (750

p cm

^{3}) and

height (30 cm) of the

cylinder are given

, we will start with the

equation for volume.

V = pr^{2}h = 30pr^{ 2}V = 750p^{}750p = 30pr^{2}

r = 5 cm

S = 2pr^{2} + 2prh

S = 2p(25) + 2p(5)(30)

S = 50p + 300 p

S = 350p cm^{2}