Find the Surface Area cylinder (2)(4)



$\begin{array}{r} h = & 2 \\ r = & 4 \end{array}$

Step 1

The surface area of a cylinder is equal to the sum of the areas of the bases each having an area of

$π \cdot r^{2}$ , plus the area of the side. The area of the side is equal to the area of a rectangle with length

$2 π r$ (the circumference of the base) times the height.

$2 π \cdot {(r a d i u s)}^{2} + 2 π \cdot (r a d i u s) \cdot (h e i g h t)$

Step 2

Substitute the values of the radius

$r = 4$ and height

$h = 2$ into the formula. Pi

$π$ is approximately equal to

$3.14$ .

$2 (π) {(4)}^{2} + 2 (π) (4) (2)$

Step 3

Simplify each term.

Raise

$4$ to the power of

$2$ .

$2 π \cdot 16 + 2 (π) (4) (2)$

Multiply

$16$ by

$2$ .

$32 π + 2 (π) (4) (2)$

Multiply

$4$ by

$2$ .

$32 π + 8 π \cdot 2$

Multiply

$2$ by

$8$ .

$32 π + 16 π$

Step 4

Add

$32 π$ and

$16 π$ .

$48 π$

Step 5

The result can be shown in multiple forms.

Exact Form:

$48 π$

Decimal Form:

$150.79644737 \dots$