To calculate the total surface area of a cylinder, you need to add the areas of its curved surface and its two circular bases. The formula for the total surface area of a cylinder is:
Total Surface Area = 2πr² + 2πrh
Where:
π (pi) is a mathematical constant approximately equal to 3.14159.
r is the radius of the circular base.
h is the height of the cylinder.
In this case, you have a cylinder with a diameter of 6 yards, which means the radius is half of that, or 6/2 = 3 yards. The height of the cylinder is given as 10 yards.
Let's substitute these values into the formula to calculate the total surface area:
Total Surface Area = 2π(3)² + 2π(3)(10)
Calculating the values inside the parentheses:
Total Surface Area = 2π(9) + 2π(30)
Simplifying further:
Total Surface Area = 18π + 60π
Combining like terms:
Total Surface Area = 78π
Now, if you want the answer in terms of yards, you can approximate π as 3.14 and calculate:
Total Surface Area ≈ 78 * 3.14
Total Surface Area ≈ 245.52 square yards
So, the total surface area of the cylinder with a diameter of 6 yards and a height of 10 yards is approximately 245.52 square yards.