Question : The external diameter of an iron pipe is 20 cm and its length is 12 cm. If the thickness of the pipe is 1 cm, find the surface area of the pipe (take $\pi=\frac{22}{7}$ ) correct to two places of decimal.
Option 1: 1,662.67 cm2
Option 2: 1,552.57 cm2
Option 3: 1,442.48 cm2
Option 4: 1,772.76 cm2
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Correct Answer: 1,552.57 cm 2
Solution :
The external radius of the iron pipe, R = $\frac{20}{2}$ = 10 cm
Internal radius of the iron pipe, r = 10 – 1 = 9 cm
Height, h = 12 cm
According to the concept, Total surface area =
$2\pi Rh + 2\pi rh + \pi(R^2−r^2) + \pi(R^2−r^2)$ where $R$ is external radius, $r$ is the internal radius, and $h$ is the height.
Total surface area = $2\pi h(R + r) + 2\pi (R^2−r^2)$
= $2\pi [12 \times (10 + 9) + (10^2 - 9^2)]$
= 1552.5714
= 1,552.57 cm
2
∴ The total surface area of the pipe is 1,552.57 cm
2
.
Hence, the correct answer is 1552.27 cm
2
.
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