Respuesta :
Answer:
correct option is 2187
Total surface area is 2,185.44 square inches.
lateral surface area is 640.56 square inches
Step-by-step explanation:
Given
radius of cylinder = 12 inches
height of cylinder = 17 inches
we will us value of pi as 3.14
surface area for cylinder consist of two part
1. lateral surface area which is gven by [tex]2\pi rl[/tex]
where r is radius of cylinder and l is height of cylinder
Thus, lateral surface area for given cylinder is
[tex]2\pi rl\\ =>2* 3.14*12*17\\=> 1281.12[/tex]
Thus, lateral surface area for given cylinder is 1281.12 square inches.
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second part of surface area is area of two base (upper and lower) of cylinder.
area of base is given by area of circle [tex]\pi r^2[/tex]
[tex]area \ of \base = \pi r^2 = 3.14*12^2\\=>area \ of \base = 3.14*144 = 452.16[/tex]
This, area of base is for one base of cylinder
since there are 2 base
area of both base will be = 2* area of one base
= 2*452.16 = 904.32.
Thus, area of base is 904.32 sq. in.
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Total surface area of cylinder = area of two base+ lateral surface area of cylinder = 1281.12 square inches + 904.32 square inches
= 2,185.44 square inches.
Thus, total surface area is 2,185.44 square inches.
lateral surface area is 640.56 square inches
but option which is closest to calculated value is 2187.
Thus, correct option is 2187
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Note: this problem can be directly solved using formula
total surface area for cylinder = [tex]2\pi r^2 + 2\pi rl[/tex]
