To find the surface area, we need to calculate the area of the two circular bases and the lateral surface area.
The formula to find the area of a circle is A = πr², where r is the radius. Since we are given the diameter, we need to divide it by 2 to find the radius.
Given:
Diameter = 2 yds
Radius = Diameter/2 = 2 yds / 2 = 1 yd
The area of each circular base is:
A_base = πr² = π(1 yd)² = π(1 yd)(1 yd) = π yd²
Next, we calculate the lateral surface area, which is equivalent to the area of a rectangle.
The lateral surface area of a cylinder is given by the formula A_lateral = 2πrh, where r is the radius and h is the height.
Given:
Height = 3 yds
Radius = 1 yd
A_lateral = 2πrh = 2π(1 yd)(3 yd) = 6π yd²
Finally, to determine the total surface area, we add the area of the two bases and the lateral surface area.
Total surface area = 2(A_base) + A_lateral = 2(π yd²) + 6π yd² = 2π yd² + 6π yd² = 8π yd²
Therefore, the surface area of the cylinder is 8π square yards.
a cylinder with a diameter of 2 yds and a height of 3 yd what is the surface area
1 answer
1 answer