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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]
[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]
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