Answer:
The volume of cylinder is [tex]864 \pi in^3[/tex]
Step-by-step explanation:
Surface area of cylinder =[tex]2 \pi r(h+r)[/tex]
Diameter of cylinder = 24 inches
Radius of cylinder =[tex]\frac{24}{2}=12 inches[/tex]
Surface area of cylinder = [tex]2 \pi 12(h+12)[/tex]
We are given that the surface area of a cylinder is S = 432π sq.in.
So,[tex]2 \pi 12(h+12)=432 \pi[/tex]
[tex]2 \times 12(h+12) = 432\\h+12=\frac{432}{2 \times 12}\\h=\frac{432}{2 \times 12}-12\\h=6[/tex]
So, height = 6 inches
Volume of cylinder = [tex]\pi r^2 h = \pi (12)^2 \times 6 =864 \pi in^3[/tex]
Hence The volume of cylinder is [tex]864 \pi in^3[/tex]
