Find the surface area of the cylinder to the nearest tenth of a square unit. Use 3.14 for π.
Answers
[tex] \qquad \qquad\large\rm{Together \: We \: Go \: Far!} \\ \qquad \qquad \sf \small{\red{♡}\:Swifties\:\red{♡}}[/tex]
Question :-
A cylinder has a radius of 4.9 ft and a height of 7.8 ft. What is the surface area of the cylinder?Answer :-
The surface area of the cylinder is 390.8044 ft².[tex] \rule{180pt}{3pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{4.9 \: ft}}\put(9,17.5){\sf{7.8 \: ft}}\end{picture}[/tex]
Solution :-
As per the provided information in the given question, we have been given that the radius of the cylinder is 4.9 ft. The height of the cylinder is 7.8 ft. We have been asked to find or calculate the surface area of the cylinder.
To calculate the surface area of the cylinder, we will use the formula below :-
[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Cylinder)} = 2\pi r^2 + 2\pi rh \:\:}}[/tex]
Substitute the given values into the above formula and solve for surface area:
[tex]\sf:\implies Surface \: Area_{(Cylinder)} = 2\pi r^2 + 2\pi rh[/tex]
[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(3.14)(4.9 \: ft)^2 + (2)(3.14)(4.9\: ft)(7.8\:ft) [/tex]
[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(3.14)(24.01\: ft^2) + (2)(3.14)(38.22\:ft^2) [/tex]
[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(75.3914 \: ft^2) + (2)(120.0108 \: ft^2) [/tex]
[tex]\sf:\implies Surface \: Area_{(Cylinder)} = 150.7828 \: ft^2 + 240.0216 \: ft^2 [/tex]
[tex]\sf:\implies \bf{Surface \: Area_{(Cylinder)} = 390.8044 \: ft^2}[/tex]
Therefore :-
The surface area of the cylinder is 390.8044 ft².[tex]\\[/tex]
Learn more about the surface area of the cylinder at https://brainly.com/question/30914875
Have a great day! <33
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