The following image is of a diatom viewed under a light microscope. The line A—B spanned 64 EPU. The same distance on the student’s drawing of the diatom measured 80 mm. What is the length (in mm) of the scale bar required to represent 40 μm on the student’s drawing?

Question

BlackTom AI · Accepted Answer

The question asks for the length of the scale bar on the student’s drawing that would represent 40 μm in real size, using the given image measurements.
Option by option analysis:

- Option: 20 mm
  This would imply a certain scale factor where a smaller drawing length corresponds to 40 μm, but there is no direct evidence in the data that the scale bar should be this short. Since AB = 80 mm on the drawing for its 64 EPU, the scale is not inherently set to 20 mm for 40 μm unless a specific, unsupported equivalence is assumed, so this option seems inconsistent with the provided proportional relationship.

- Option: 128 mm
  A length of 128 mm would indicate a much larger drawing length per 40 μm, requiring a scale factor that greatly exaggerates the real size. Given AB maps 64 EPU to 80 mm, moving to 40 μm would not reasonably double the length to 128 mm without contradicting the observed proportionality between EPU and drawing length. This makes 128 mm implausible under the same scale.

- Option: 40 mm
  If 1 EPU on the drawing corresponds to a fixed drawing length, and the 40 μm real size is to be represented with a scale bar that is proportional to the AB measurement (64 EPU → 80 mm), then the scale can be set so that 40 μm corresponds to 40 mm on the drawing. This preserves a consistent, linear scale from the real size to the drawing size across the measured region, aligning with the idea that 40 μm is represented by a moderate drawing length matching the AB-to-drawing proportion.

- Option: 80 mm
  This would double the length of the proposed 40 μm representation compared with the AB reference (80 mm for 64 EPU). Without a stated reason to double, and given the AB measurement of 64 EPU → 80 mm, using 80 mm for 40 μm would violate the implied uniform scale unless 40 μm corresponds to exactly the same numerical drawing length as 80 mm, which is unlikely given the proportional relationships usually used in such questions.

- Option: 64 mm
  While 64 mm is a round number close to the AB-derived 80 mm, selecting 64 mm would require a specific, different scale than the one implied by AB (64 EPU → 80 mm). There is no information supporting that 40 μm should map to 64 mm under the same scale, so this option is not well supported by the given proportion.

In summary, the only option that coherently follows from a single, consistent proportional relationship between the AB measurement (in EPU) and its drawing length (80 mm for 64 EPU) while translating 40 μm into a drawing length using the same scale is 40 mm. The proportional reasoning yields a scale bar length that keeps the same linear correspondence between real size (μm) and drawing size (mm).

The following image is of a diatom viewed under a light microscope. The line A—B spanned 64 EPU. The same distance on the student’s drawing of the diatom measured 80 mm. What is the length (in mm) of the scale bar required to represent 40 μm on the student’s drawing?Single choice

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