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:

$150.79644737 \dots$

Find the Surface Area cylinder (2)(4)

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