Answer:
To calculate the surface area and volume of a cylinder, we can use the following formulas:
a) Surface Area of a Cylinder:
The surface area of a cylinder consists of two circles (top and bottom) and the curved surface area.
The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
Where:
SA = Surface Area
r = Radius of the base (half the diameter)
h = Height of the cylinder
Given that the diameter is 16 yards, the radius is half of that, so r = 8 yards. The height is 20 yards.
Substituting the values into the formula, we get:
SA = 2π(8)² + 2π(8)(20)
= 2π(64) + 2π(160)
= 128π + 320π
= 448π
So, the surface area of the cylinder is 448π square yards.
b) Volume of a Cylinder:
The formula for the volume of a cylinder is:
V = πr²h
Using the same values for the radius (r = 8 yards) and height (h = 20 yards), we can calculate the volume:
V = π(8)²(20)
= 64π(20)
= 1280π
The volume of the cylinder is 1280π cubic yards.