Answer:
30.79 cm^2 ( to nearest hundredth).
Explanation:
Height = 3/2 of the radius ( as the ratio of r to h = 2:3.).
h = 3r/2. or 1.5r.
Volume of the cylinder = π r^2 h = 12.936
So π r^2 1.5r = 12.936
r^3 = 12.936 / (π * 1.5r)
r = 1.4 and h = 1.4 * 3/2 = 2.1
Total surface area 2π r^2 + 2πrh
= 2π(1.4)^2 + 2π1.4*2.1
= 9.8π
= 30.79 cm^2 answer