Answer:
Part a) The lateral area is [tex]4r^{2} \pi \ in^{2}[/tex]
Part b) The area of the two bases together is [tex]2r^{2} \pi\ in^{2}[/tex]
Part c) The surface area is [tex]6r^{2} \pi\ in^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of a right cylinder is equal to
[tex]SA=LA+2B[/tex]
where
LA is the lateral area
B is the area of the base of cylinder
we have
[tex]r=r\ in[/tex]
[tex]h=2r\ in[/tex]
Part a) Find the lateral area
The lateral area is equal to
[tex]LA=2\pi rh[/tex]
substitute the values
[tex]LA=2\pi r(2r)[/tex]
[tex]LA=4r^{2} \pi\ in^{2}[/tex]
Part b) Find the area of the two bases together
The area of the base B is equal to
[tex]B=r^{2} \pi\ in^{2}[/tex]
so
the area of the two bases together is
[tex]2B=2r^{2} \pi\ in^{2}[/tex]
Part c) Find the surface area of the cylinder
[tex]SA=LA+2B[/tex]
we have
[tex]LA=4r^{2} \pi\ in^{2}[/tex]
[tex]2B=2r^{2} \pi\ in^{2}[/tex]
substitute
[tex]SA=4r^{2} \pi+2r^{2} \pi=6r^{2} \pi\ in^{2}[/tex]
