Scale Drawings and Maps Lesson 110 Scale Drawings and Maps

Vocabulary Scale is the ratio between two corresponding measurements Scale drawing is a drawing that uses a scale to represent an object as being smaller or larger than the actual object Where are some places you have seen a scale drawing? Maps Blueprints Models

The actual hind leg of a grasshopper is 1 The actual hind leg of a grasshopper is 1.5 inches long and its antennae are 0.25 inches long. If a scale drawing for the grasshopper is 1 in. to 4 cm, what are these lengths in the drawing? 𝑎𝑐𝑡𝑢𝑎𝑙 𝑠𝑐𝑎𝑙𝑒 𝑑𝑟𝑎𝑤𝑖𝑛𝑔 = 1 𝑖𝑛 4 𝑐𝑚 1 4 = 1.5 𝑙 𝑙=6 𝑐𝑚 1 4 = 0.25 𝑎 𝑎=1 𝑐𝑚

A helium atom has an atomic radius of 31 picometers A helium atom has an atomic radius of 31 picometers. If Emily models the helium atom with a scale of 2 pm : 3cm, what is the radius of the model. 𝑎𝑐𝑡𝑢𝑎𝑙 𝑠𝑐𝑎𝑙𝑒 𝑚𝑜𝑑𝑒𝑙 = 2 𝑝𝑚 3 𝑐𝑚 2 3 = 31 𝑚 2𝑚=93 𝑚=46.5 𝑐𝑚 If this question was extended to find the volume, what ratio would we need to use? 8 :27 The actual conversion is 1pm : 1x10-12m, but this is unnecessary since we are just converting to the size of the model

Adina lives 145 meters from Darren. If Adina is 543 Adina lives 145 meters from Darren. If Adina is 543.75 meters from the park, how far would that be on the map? Start by finding the scale 𝑠𝑐𝑎𝑙𝑒 𝑚𝑎𝑝 𝑎𝑐𝑡𝑢𝑎𝑙 = 2 𝑐𝑚 145 𝑚 2 145 = 𝑚 543.75 145𝑚=1087.5 𝑚=7.5 𝑐𝑚

Questions/Review Commonly scales are in the form of b to 1 or 1:b, with one of the units equal to one So let’s revisit 2 of the scales we used on our examples today 2 𝑝𝑚 3 𝑐𝑚 & 2 𝑐𝑚 145 𝑚 2 𝑝𝑚 3 𝑐𝑚 = 1 𝑝𝑚 1.5 𝑐𝑚 1 𝑝𝑚 :1.5 𝑐𝑚 2 𝑐𝑚 145 𝑚 = 1 𝑐𝑚 72.5 𝑚 1 𝑐𝑚 to 72.5 𝑚