Determine the exact surface area of the cylinder in terms of π.
cylinder with radius labeled 1 and one fourth centimeters and a height labeled 3 and three fourths centimeters
39 and one fourth times pi square centimeters
14 and one sixteenth times pi square centimeters
12 and one half times pi square centimeters
10 and 15 sixteenths times pi square centimeters
The formula to calculate the surface area of a cylinder is given by:
A = 2πrh + 2πr^2
where r is the radius and h is the height of the cylinder.
In this case, the radius is 1 and 1/4 cm, which can be written as 5/4 cm.
The height is 3 and 3/4 cm, which can be written as 15/4 cm.
Substituting these values into the formula, we get:
A = 2π(5/4)(15/4) + 2π(5/4)^2
A = 2π(75/16) + 2π(25/16)
A = (150π + 50π) / 16
A = 200π / 16
Simplifying the fraction, we get:
A = 25π / 2
The exact surface area of the cylinder in terms of π is 25π / 2 square centimeters. So, the correct answer is:
10 and 15/16 times π square centimeters.