Find the surface area of the cylinder. Round to the nearest tenths.

The surface area of the cylinder is 251.2cm²

Step-by-step explanation:

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

radius = half of diameter

r = 10/2 = 5cm

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

a = area

r = radius = 5cm

π = 3.14

a = π * r²

we replace with the known values

a = 3.14 * (5cm)²

a = 3.14 * 25cm²

a = 78.5cm²

The area of the circle is 78.5cm²

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

a = area  =

h = heighti = 3cm

r = radius = 5cm

π = 3.14

a = 2 * π * r * h

we replace with the known values

a = 2 * 3.14 * 5cm * 3cm

a = 6.28 * 15cm²

a = 94.2cm²

The lateral area of the cylinder is 94.2cm²

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

94.2cm²  + (2 * 78.5cm²) = 251.2cm²

The surface area of the cylinder is 251.2cm²

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