Find the surface area of a cylinder with a surface area of 7 yards and height of 8 yards use the approximation 3.14 for pi.
The formula to calculate the surface area of a cylinder is given by:
Surface Area = 2πr^2 + 2πrh
We are given the following information:
Surface Area = 7 yards
Height (h) = 8 yards
Let's assume the radius of the cylinder as r. We need to find the value of r.
Substituting the given values into the formula, we get:
7 = 2 * π * r^2 + 2 * π * r * 8
Using the approximation π ≈ 3.14, the equation becomes:
7 = 2 * 3.14 * r^2 + 2 * 3.14 * r * 8
Divide the entire equation by 2 * 3.14 to isolate the term with r^2:
7 / (2 * 3.14) = r^2 + r * 8
3.54 = r^2 + 8r
Rearranging the equation:
r^2 + 8r - 3.54 = 0
Now, we can solve this quadratic equation to find the values of r.
Using the quadratic formula:
r = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = 8, and c = -3.54.
r = (-8 ± √(8^2 - 4 * 1 * -3.54)) / (2 * 1)
r = (-8 ± √(64 + 14.16)) / 2
r = (-8 ± √(78.16)) / 2
r ≈ (-8 ± 8.84) / 2
Solving for the two possible values of r:
r ≈ (-8 + 8.84) / 2 ≈ 0.42
r ≈ (-8 - 8.84) / 2 ≈ -8.42 (Not a valid answer since radius cannot be negative)
Therefore, the radius (r) of the cylinder is approximately 0.42 yards.
Now, substitute this value of r and the given height (h) into the formula to find the surface area:
Surface Area = 2 * π * r^2 + 2 * π * r * h
Surface Area = 2 * 3.14 * (0.42)^2 + 2 * 3.14 * 0.42 * 8
Surface Area ≈ 2.66 + 21.024
Surface Area ≈ 23.684 square yards
Thus, the surface area of the given cylinder is approximately 23.684 square yards.