h=9r=2

The surface area of a cylinder is equal to the sum of the areas of the bases each having an area of π⋅r2, plus the area of the side. The area of the side is equal to the area of a rectangle with length 2πr (the circumference of the base) times the height.

2π⋅(radius)2+2π⋅(radius)⋅(height)

Substitute the values of the radius r=2 and height h=9 into the formula. Pi π is approximately equal to 3.14.

2(π)(2)2+2(π)(2)(9)

Multiply 2 by (2)2 by adding the exponents.

Move (2)2.

(2)2⋅2π+2(π)(2)(9)

Multiply (2)2 by 2.

Raise 2 to the power of 1.

(2)2⋅21π+2(π)(2)(9)

Use the power rule aman=am+n to combine exponents.

22+1π+2(π)(2)(9)

22+1π+2(π)(2)(9)

Add 2 and 1.

23π+2(π)(2)(9)

23π+2(π)(2)(9)

Raise 2 to the power of 3.

8π+2(π)(2)(9)

Multiply 2 by 2.

8π+4π⋅9

Multiply 9 by 4.

8π+36π

8π+36π

Add 8π and 36π.

44π

The result can be shown in multiple forms.

Exact Form:

44π

Decimal Form:

138.23007675…

Find the Surface Area cylinder (9)(2)