Question

Which is closest to the total surface area of a cylinder with a radius of 5 inches and a height that is equal to its diameter?

Answer 1

the question does not present the options, however this does not prevent its resolution

we know that
[surface area of the cylinder]=2*area of the base+perimeter of base*height
r=5 in
diameter=2*r----> 2*5----> 10 in
height=10 in

area of the base=pi*r²----> pi*5²----> 78.5 in²

perimeter of the base=2*pi*r----> 2*pi*5----> 31.4 in

[surface area of the cylinder]=2*78.5+31.4*10----> 471 in²

the surface area of the cylinder is 471 in²

Answer 2

For this case, the surface area of the cylinder is given by:
A = 2 * pi * r * h + 2 * pi * r ^ 2
Where.
r: cylinder radius
h: cylinder height
Substituting values we have:
A = 2 * 3.14 * 5 * (2 * 5) + 2 * 3.14 * 5 ^ 2
A = 471
Answer:
The total surface area of the cylinder is:
A = 471