A metal cylindrical cannister is 1' 3"long and has a diameter of 4 inches. What is the total surface area of the cylinder?
A=2πrh+2πr2
radius=2 (d/2)
h=1.3
A=41.47
Double check this. :)
h = 15 inches, not 1.3
1’3” = 15 inches & Radius = 2 in
SA = 2πr² + 2πrh
= 2 (π) (2²) + 2 (π) (2) (15)
= 213.63in²
To find the total surface area of a cylinder, we need to calculate the area of the two circular bases and the lateral surface area.
1. Calculate the area of the circular bases:
The formula to find the area of a circle is A = πr², where A is the area and r is the radius.
Given that the diameter of the cylinder is 4 inches, the radius (r) is half of that, so r = 2 inches.
Calculate the area of one circular base using the formula A_base = πr².
A_base = π(2 inches)²
2. Calculate the lateral surface area:
The lateral surface area of a cylinder can be found using the formula A_lateral = 2πrH, where H is the height of the cylinder.
Given that the height of the cylinder is 1 foot 3 inches (15 inches), and the radius (r) is 2 inches, we can compute A_lateral.
A_lateral = 2π(2 inches)(15 inches)
3. Add the areas together:
The total surface area of the cylinder is the sum of the area of the two circular bases (A_base) and the lateral surface area (A_lateral).
Total surface area = 2(A_base) + A_lateral
Now plug in the values and calculate the total surface area.