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I am trying to figure out a questions but i need to know the formula for the surface area of a disk. if anyone could help me out it would be great.

The question i am trying to answer is: " the concrete pipe shown in the diagram has the following measurements: t(thickness of the pipe): 30mm d(diameter): 18cm and l(length):27cm. i have to figure out the surface area of both sides of this pipe. the sides are shaped like disks.

sorry the diagram is upside down but its really hard trying to take a pic with a macbook enter image description here

samantha
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  • I don't understand what is called the surface area of a disk? I suppose you mean the surface area of a cylinder, since you mention a pipe. If it is the case, it's simply $\pi\times \text{diameter}$. – Bernard Feb 15 '15 at 00:56
  • @Bernard $\pi \times \textrm{diameter}$ is the circumference. I imagine you meant $\pi \times \textrm{diameter} \times \textrm{length}$. – mathmandan Feb 15 '15 at 01:09
  • @mathmandan: thanks for pointing the typo. I can't edit my comment any more, but I've written an answer anyway… – Bernard Feb 15 '15 at 01:17
  • This is a cylinder, not a disk. – Michael Hardy Feb 15 '15 at 02:13
  • You probably mean the area of a ring, I can't imagine you can't compute the area of a disk. –  Jun 17 '16 at 21:00
  • How hard is it to flip an image taken with a MacBook ? –  Jun 17 '16 at 21:00

2 Answers2

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Lateral area of a cylinder of diameter $d$ and length $l$: $\pi d l$.

Area of a disk of diameter $d$: $\,\pi\dfrac{d^2}4$, hence the area of an annulus between a disk of diameter $d$ and a disk of diameter $d'$: $\dfrac{\pi(d^2-d'^2)}4$.

Total area, taking into account the inner cylinder:

$$\pi(d+d')l+2\pi\frac{d^2-d'^2}4=\pi(d+d')\Bigl(l+\frac{d-d'}2\Bigr).$$

Now $d'=d-2t$. There remains to simplify the results and compute numerically.

Bernard
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You have two cylinders and two annuli to find the surface area of. The area of a cylinder is $2\pi rh$, where $r$ is the radius and $h$ is the height. You can imagine unrolling the cylinder to a rectangle. Can you find the inner and outer radii of your pipe? For the annuli, imagine filling them in to form a circle. The surface of the circle is $\pi r^2$, so the surface of the annulus is the difference of two circles: $\pi(r_1^2-r_2^2)$, where $r_1$ is the outer radius and $r_2$ is the inner one.

Ross Millikan
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