What is the surface area, in square inches, of a closed cylindrical tank with a radius of 4 inches and a height of 10 inches?

A. 16π B. 32π C. 80π D. 112π E. 128π

(D) The cylinder can be broken down into two circular caps and a rectangular body whose length is equal to the circumference of each circular cap. Each circular cap will have a surface area of: 4²π, or 16π. Since we have two such caps, the sum of their areas equals 32π square inches.

Next, we want to determine the surface area of the cylindrical body. The latter is equal to the circumference of the circle multiplied by the height, 8π × (10) = 80π square inches. So, the cylindrical surface area is equal to the sum of the areas we found: 80π + 32π = 112π square inches.

The answer is choice (D) ----------

Regarding this answer, why does the both cap surfaces must be added to the surface of the length instead multiply both by the latter?

When you deal with surface or volume make sure you get right dimensions at the end. If you multiply one surface area by another surface are you will not get a surface area, because in this case you would get:

That doesn’t make any sense and should ring a bell that calculations are incorrect. On the other hand, when you calculate a surface area of a complicated figure you can break it into simpler ones and then sum up the figures. In this case the dimensions are Ok:

It is very important in this kind of problems to separate components of a large figure into smaller parts, then to calculate each part separatelly and finally add them all together.

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