Question

find the surface area of each cylinder. round your answer to two decimal places.(use $pi = 3.14$)1)surface area = _____2)surface area = ___3)surface area = ___4)surface area = ___5)surface area = ___6)surface area = ___7)surface area = ___8)surface area = ___9)surface area = _____

Explanation:

The formula for the total surface area of a cylinder is $SA = 2\pi r^2 + 2\pi rh$, where $r$ is the radius of the base, $h$ is the height of the cylinder, and $\pi=3.14$.

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1) Cylinder with $r=5.2$ in, $h=5.5$ in

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(5.2)^2$
$= 6.28\times27.04 = 169.8112$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times5.2\times5.5$
$= 6.28\times28.6 = 179.608$

Step3: Sum the two areas

$SA = 169.8112 + 179.608 = 349.4192$

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2) Cylinder with $r=3.7$ yd, $h=7.1$ yd

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(3.7)^2$
$= 6.28\times13.69 = 85.9732$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times3.7\times7.1$
$= 6.28\times26.27 = 164.9756$

Step3: Sum the two areas

$SA = 85.9732 + 164.9756 = 250.9488$

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3) Cylinder with $r=\frac{7.6}{2}=3.8$ ft, $h=7.2$ ft

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(3.8)^2$
$= 6.28\times14.44 = 90.6832$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times3.8\times7.2$
$= 6.28\times27.36 = 171.8208$

Step3: Sum the two areas

$SA = 90.6832 + 171.8208 = 262.504$

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4) Cylinder with $r=12.4$ yd, $h=14.2$ yd

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(12.4)^2$
$= 6.28\times153.76 = 965.6128$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times12.4\times14.2$
$= 6.28\times176.08 = 1105.7824$

Step3: Sum the two areas

$SA = 965.6128 + 1105.7824 = 2071.3952$

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5) Cylinder with $r=6.7$ ft, $h=9.8$ ft

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(6.7)^2$
$= 6.28\times44.89 = 281.9092$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times6.7\times9.8$
$= 6.28\times65.66 = 412.3448$

Step3: Sum the two areas

$SA = 281.9092 + 412.3448 = 694.254$

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6) Cylinder with $r=4.3$ in, $h=8.6$ in

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(4.3)^2$
$= 6.28\times18.49 = 116.1172$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times4.3\times8.6$
$= 6.28\times36.98 = 232.2344$

Step3: Sum the two areas

$SA = 116.1172 + 232.2344 = 348.3516$

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7) Cylinder with $r=2.2$ in, $h=10.3$ in

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(2.2)^2$
$= 6.28\times4.84 = 30.3952$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times2.2\times10.3$
$= 6.28\times22.66 = 142.3048$

Step3: Sum the two areas

$SA = 30.3952 + 142.3048 = 172.7$

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8) Cylinder with $r=\frac{7.8}{2}=3.9$ ft, $h=11.3$ ft

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(3.9)^2$
$= 6.28\times15.21 = 95.5188$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times3.9\times11.3$
$= 6.28\times44.07 = 276.7596$

Step3: Sum the two areas

$SA = 95.5188 + 276.7596 = 372.2784$

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9) Cylinder with $r=9.4$ yd, $h=8.4$ yd

Step1: Calculate base areas

$2\pi r^2 = 2\times3.14\times(9.4)^2$
$= 6.28\times88.36 = 554.9008$

Step2: Calculate lateral surface area

$2\pi rh = 2\times3.14\times9.4\times8.4$
$= 6.28\times78.96 = 495.8688$

Step3: Sum the two areas

$SA = 554.9008 + 495.8688 = 1050.7696$

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Answer:

1. $349.42$ square inches
2. $250.95$ square yards
3. $262.50$ square feet
4. $2071.40$ square yards
5. $694.25$ square feet
6. $348.35$ square inches
7. $172.70$ square inches
8. $372.28$ square feet
9. $1050.77$ square yards