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Chapter 9: Problem 65

Select the best estimate for the measure of the area of the object described. The area of the face of a small coin a. \(6 \mathrm{~mm}^{2}\) b. \(6 \mathrm{~cm}^{2}\) c. \(6 \mathrm{dm}^{2}\)

Short Answer

Expert verified
\(6 \mathrm{~mm^{2}}\)

Step by step solution

01

Understand the size of units

The first thing to understand is the difference in size between square millimeters (mm虏), square centimeters (cm虏) and square decimeters (dm虏). A millimeter square is the area of a square that has 1 mm on each side, similarly for cm虏 and dm虏. In terms of size, \(1 \mathrm{~dm^{2}} = 10000 \mathrm{~mm^{2}}\) and \(1 \mathrm{~dm^{2}} = 100 \mathrm{~cm^{2}}\). So, a square decimeter is much larger than a square centimeter, and a square centimeter is much larger than a square millimeter.
02

Estimate the appropriate size

The exercise asks for the best estimate, so it does not require exact measurements. Since this is a small coin, it's area won't be very big. In fact, if one imagines a square decimeter, it is quite large compared to a small coin. So, \(6 \mathrm{~dm^{2}}\) is probably too big. The same goes for a square centimeter. Although it is smaller than a square decimeter, it is still quite large compared to a small coin. So, \(6 \mathrm{~cm^{2}}\) is also likely too big. Therefore, given the sizes of the other options, \(6 \mathrm{~mm^{2}}\) is the most likely option.

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