Answer:
2656.31 [tex]cm^{2}[/tex]
Step-by-step explanation:
To calculate the surface area, we need to find the area of all the faces, and add them together.
The faces of the cylinder are: the rectangular base, the curved top, and the two semicircles on the side.
Rectangular base:
A = length x width
A = 29.3 x 16.2
A = 474.66
Two semicircles:
A = [tex]\pi[/tex] x [tex]radius^{2}[/tex] (I'm using the formula for a circle, because the two semicircles are identical, so together they form a circle)
radius = 29.3/2 = 14.65
A = [tex]\pi[/tex] x [tex]14.65^{2}[/tex]
A = 674.256 (rounded to 3 decimal places)
Curved top:
The curved top, when flattened out, becomes a rectangle with a length of 16.2. The width is equal to half the circumference of the circle formed by the two semicircles.
To find the width, use the circumference (C) formula.
C = [tex]\pi[/tex] x diameter
diameter = 29.3
C = [tex]\pi[/tex] x 29.3
C = 93.049 (rounded to 3 DP)
Area (of curved top) = length x width
A = 16.2 x 93.049
A = 1507.394 (rounded to 3 DP)
Surface Area
SA = 474.66 + 674.256 + 1507.394
SA = 2656.31 [tex]cm^{2}[/tex]
