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?

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
 
 The total surface area of the cylinder is:
 A = 471

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