Answer:
Surface Area = 10π
Step by step solved:
To find the exact surface area of a cylinder with a radius of 1 3/4 and height of 3 1/4, we can use the formula:
Surface Area = 2πr^2 + 2πrh
where r is the radius and h is the height.
Substituting the given values, we get:
Surface Area = 2π(1 3/4)^2 + 2π(1 3/4)(3 1/4)
First, let's simplify the terms inside the parentheses:
1 3/4 = 7/4
3 1/4 = 13/4
Now we can substitute:
Surface Area = 2π(7/4)^2 + 2π(7/4)(13/4)
Simplifying the terms inside the parentheses:
(7/4)^2 = 49/16
(7/4)(13/4) = 91/16
Substituting these values:
Surface Area = 2π(49/16) + 2π(91/16)
Simplifying the terms inside the parentheses:
(49/16)π = (7/4)π
(91/16)π = (13/4)π
Substituting these values:
Surface Area = 2(7/4)π + 2(13/4)π
Simplifying:
Surface Area = 14/4 π + 26/4 π
Surface Area = 40/4 π
Surface Area = 10π
Therefore, the exact surface area of the cylinder is 10π square units.