Basic Math Examples

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\begin{array}{r} h = & 5 \\ r = & 2 \end{array}

$\begin{array}{r} h = & 5 \\ r = & 2 \end{array}$

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}

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

2 π r

$2 π r$ (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)

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

Step 2

Substitute the values of the radius

r = 2

$r = 2$ and height

h = 5

$h = 5$ into the formula. Pi

π

$π$ is approximately equal to

3.14

$3.14$ .

2 (π) {(2)}^{2} + 2 (π) (2) (5)

$2 (π) {(2)}^{2} + 2 (π) (2) (5)$

Step 3

Simplify each term.

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Step 3.1

Multiply

2

$2$ by

{(2)}^{2}

${(2)}^{2}$ by adding the exponents.

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Step 3.1.1

Move

{(2)}^{2}

${(2)}^{2}$ .

{(2)}^{2} \cdot 2 π + 2 (π) (2) (5)

${(2)}^{2} \cdot 2 π + 2 (π) (2) (5)$

Step 3.1.2

Multiply

{(2)}^{2}

${(2)}^{2}$ by

2

$2$ .

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Step 3.1.2.1

Raise

2

$2$ to the power of

1

$1$ .

{(2)}^{2} \cdot 2^{1} π + 2 (π) (2) (5)

${(2)}^{2} \cdot 2^{1} π + 2 (π) (2) (5)$

Step 3.1.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

2^{2 + 1} π + 2 (π) (2) (5)

$2^{2 + 1} π + 2 (π) (2) (5)$

2^{2 + 1} π + 2 (π) (2) (5)

$2^{2 + 1} π + 2 (π) (2) (5)$

Step 3.1.3

Add

2

$2$ and

1

$1$ .

2^{3} π + 2 (π) (2) (5)

$2^{3} π + 2 (π) (2) (5)$

2^{3} π + 2 (π) (2) (5)

$2^{3} π + 2 (π) (2) (5)$

Step 3.2

Raise

2

$2$ to the power of

3

$3$ .

8 π + 2 (π) (2) (5)

$8 π + 2 (π) (2) (5)$

Step 3.3

Multiply

2

$2$ by

2

$2$ .

8 π + 4 π \cdot 5

$8 π + 4 π \cdot 5$

Step 3.4

Multiply

5

$5$ by

4

$4$ .

8 π + 20 π

$8 π + 20 π$

8 π + 20 π

$8 π + 20 π$

Step 4

Add

8 π

$8 π$ and

20 π

$20 π$ .

28 π

$28 π$

Step 5

The result can be shown in multiple forms.

Exact Form:

28 π

$28 π$

Decimal Form:

87.96459430 \dots

$87.96459430 \dots$

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