Answer:
- The area of the two bases is 32π in².
- The lateral area is 40π in².
- The total surface area is 72π in².
Step-by-step explanation:
1. The base of the cylinder is a circle, therefore, you can apply the formula for calculate the area of a circle:
[tex]A=r^{2}\pi[/tex]
Where [tex]r[/tex] is the radius.
Then the area of the base is:
[tex]A_b=(4in)^{2}\pi=16in^{2}[/tex]
Multiply by 2 to obtain the area of the two bases:
[tex]A_{bases}=2(16\pi)=32\pi[/tex][tex]in^{2}[/tex]
2. The lateral area is (Where [tex]h[/tex] is the height):
[tex]LA=2rh\pi=2(4in)(5in)\pi=40\pi[/tex][tex]in^{2}[/tex]
3. The total surface area is calculated with the formula:
[tex]A_t=2r^{2}\pi+h(2r\pi)[/tex]
Where [tex]h[/tex] is the height.
Then:
[tex]A_t=2\pi(4in)^{2}+\pi(5in)(2)(4in)=72\pi[/tex][tex]in^{2}[/tex]
