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The radius of the base of a cylinder is 38 mm and its height is 51 mm. Find the surface area of the cylinder in terms of [tex]$\pi$[/tex].

A. [tex]$6764 \pi \, \text{mm}^2$[/tex]
B. [tex][tex]$6853 \pi \, \text{mm}^2$[/tex][/tex]
C. [tex]$6713 \pi \, \text{mm}^2$[/tex]
D. [tex]$6726 \pi \, \text{mm}^2$[/tex]


Sagot :

To find the surface area of a cylinder, you need to know both the radius of its base and its height. For a cylinder with a radius [tex]\( r \)[/tex] and height [tex]\( h \)[/tex], the surface area [tex]\( A \)[/tex] can be calculated using the formula:

[tex]\[ A = 2\pi r (h + r) \][/tex]

Given:
- Radius [tex]\( r = 38 \)[/tex] mm
- Height [tex]\( h = 51 \)[/tex] mm

Substituting the given values into the formula, we have:

[tex]\[ A = 2\pi \times 38 \times (51 + 38) \][/tex]

First, compute the sum inside the parentheses:

[tex]\[ 51 + 38 = 89 \][/tex]

Next, multiply the radius by this sum and then by [tex]\( 2\pi \)[/tex]:

[tex]\[ 2 \pi \times 38 \times 89 = 2 \times 38 \times 89 \pi \][/tex]

Calculate [tex]\( 2 \times 38 \)[/tex]:

[tex]\[ 2 \times 38 = 76 \][/tex]

Then multiply this result by 89:

[tex]\[ 76 \times 89 = 6764 \][/tex]

Finally, multiply by [tex]\( \pi \)[/tex]:

[tex]\[ 6764 \pi \, \text{mm}^2 \][/tex]

Therefore, the surface area of the cylinder is:

[tex]\[ 6764 \pi \, \text{mm}^2 \][/tex]

The correct answer is:

[tex]\[ 6764 \pi \, \text{mm}^2 \][/tex]