Answer:
As given below
Given data:
A advertising column is consist of a cylindrical part surmounted by hemisphere part on the top
base diameter of the column 2r = 7 feet
radius of the column r = 7/2 = 3.5 feet
height of the cylindrical part h = 11 feet
Step-by-step explanation:
(i) Find the surface area of cylindrical part of column?
and Find the total surface area of advertising column?
surface area of the cylindrical part = 2πrh
= [tex]2(\frac{22}{7} ) 3.5( 11)[/tex]
= 22(11) = 242 ft²
total surface area of advertising column
= surface area of cylindrical part + curved surface area of hemisphere
here curved surface area of hemisphere = 2 π r²
= [tex]2(\frac{22}{7} )(3.5)(3.5)[/tex] = 22(3.5) = 77 ft²
total surface area of the advertising column = 242 ft²² + 77 ft² = 319 ft²
(ii) Find the volume of advertising column?
volume of the advertising column
= volume of cylindrical part + volume of hemisphere
volume of cylindrical part = π r² h
= [tex]\frac{22}{7} (3.5)(3.5) (11)[/tex]
= 11(3.5) (11) = 423.5 ft³
volume of hemisphere = [tex]\frac{2}{3} \pi r^{3}[/tex]
= [tex](\frac{2}{3} )(\frac{22}{7} )(3.5)(3.5)(3.5)[/tex]
= (0.66)(11) (3.5)(3.5) = 88.935 ft³
volume of the advertising column = 423.5 + 88.935
= 512.435 ft³