#### Answer

65 $\pi$ $cm^{2}$

#### Work Step by Step

V = $\frac{\pi r^{2} h}{3}$
h = $\frac{3 V}{ \pi r^{2}}$
h = $\frac{3 \times 100\pi cm^{3}}{ \pi 25 cm^{2}}$
h = 12 cm
a = $\sqrt (h^{2} + r^{2} )$
a = $\sqrt (144 cm^{2} + 25 cm^{2}) $
a = 13 cm
Lateral area = $\pi$ r a
Lateral area = $\pi$ $\times$ 5 cm $\times$ 13 cm
Lateral area = 65 $\pi$ $cm^{2}$