Find the surface area of a cylinder with a base radius of 4 yd and a height of 9 yd.

The surface area of the cylinder is 326.56yd²

Step-by-step explanation:

To solve this problem we have to calculate the circle area and the lateral area

To calculate the area of the circle we use the following formula

a = area

r = radius = 4yd

π = 3.14

a = π * r²

we replace with the known values

a = π * (4yd) ²

a = π * 16yd²

a = 50.24yd²

The area of the circle is 50.24yd²

To calculate the lateral area of the cylinder we use the following formula

a = area

h = heighti = 9yd

r = radius = 4yd

π = 3.14

a = 2 * π * r * h

we replace with the known values

a = 2 * 3.14 * 4yd * 9yd

a = 6.28 * 36yd²

a = 226.08yd²

The lateral area of the cylinder is 226.08yd²

Now we add the lateral area of the cylinder with 2 times the area of the circle and obtain the area of the cylinder

226.08yd² + (2 * 50.24yd²) = 326.56yd²

The surface area of the cylinder is 326.56yd²