We are given that a log is cut lengthwise through its center and we want to find the surface area of one of the halves. To do this let's sketch a diagram of one of the halves.
First let's convert feet to inches, as we want to have all dimensions in the same unit. Recall that there are 12 inches in one foot.
Now let's notice that the surface area of one of the halves is the sum of half of the surface area of a cylinder and the area of a rectangle.
1/2 S.A.+A_r
Let's start with evaluating the first part. We will use the fact that the radius is one half of the diameter.
1/2(2π( 182)( 36)+2π ( 182)^2)
Let's simplify the above expression.
Half of the area of a cylinder is approximately 1272 square inches. Next, let's find the area of a rectangle that has a width of 18 inches and a length of 36 inches.
18* 36=648
The area of the rectangle is 648 square inches. Finally, we will add the half of the surface area and the area of the rectangle.
1272+ 648=1920
The surface area of one of the halves is approximately 1920 square inches.
