Answer:
Is needed [tex]452.32\ ft^{2}[/tex] of sheet metal to build this tank
Step-by-step explanation:
we know that
To find how much sheet metal is needed to build this tank including the top, calculate the lateral area of the cone plus the lateral area of the cylinder plus the area of the top of the cylinder
[tex]A=\pi rl+2\pi rh1+\pi r^{2}[/tex]
we have
[tex]r=5\ ft[/tex]
[tex]h1=8\ ft[/tex] ----> height of the cylinder
[tex]h2=6\ ft[/tex] ----> height of the cone
Find the slant height of the cone l
Applying Pythagoras Theorem
[tex]l^{2}=r^{2}+h2^{2}[/tex]
substitute
[tex]l^{2}=5^{2}+6^{2}[/tex]
[tex]l^{2}=61[/tex]
[tex]l=\sqrt{61}\ ft[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]A=(3.14)(5)(\sqrt{61})+2(3.14)(5)(8)+(3.14)(5)^{2}[/tex]
[tex]A=122.62+251.2+78.5=452.32\ ft^{2}[/tex]
