Scale Drawings & Proportions

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Presentation transcript:

Scale Drawings & Proportions

A scale drawing is a two-dimensional drawing of an object that is proportional to the object. A scale model is a three-dimensional model that is proportional to the object. A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

SCALE DRAWINGS A scale drawing is a drawing of an object with dimensions proportional to those of the actual object. To find lengths from scale drawings, set up and solve proportions.

There are many uses of ratios and proportions There are many uses of ratios and proportions. We use them in map reading, making scale drawings and models, solving problems.

The most recognizable use of ratios and proportions is drawing models and plans for construction. Scales must be used to approximate what the actual object will be like.

Example 1: Find Actual Measurements A set of landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4 feet. What is the width of the actual flower bed? Let x represent the actual width of the flower bed. Write and solve a proportion. Plan width----> 1 inch = 6.5 inches<---plan width Actual width--> 4 feet x feet <-----actual width 1x = 46.5 cross products x= 26 The actual flower bed width is 26 feet.

SCALE DRAWINGS USING PROPORTIONS ¼ in = 5 ft is a scale for a rock band’s concert stage. The scale length of the drum stand is 1 inch. What is the actual length of the drum stand? Cross multiply. Divide by .25 .25 .25

SCALE DRAWINGS USING PROPORTIONS ¼ in = 5 ft is a scale for a rock band’s concert stage. The actual length of the microphone stand is 4.5 feet. What is the length mic stand in the drawing? Cross multiply. Divide by 5. 5 5

SCALE DRAWINGS USING PROPORTIONS Given a scale of 0.5 in = 4 ft, find the actual length for A and find the drawing length for B. 4 4 .5 .5

A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale? 1 cm x m 2 cm 8 m Set up proportion using scale length . actual length = 1  8 = x  2 Find the cross products. 8 = 2x 4 = x Divide both sides by 2. The scale is 1 cm:4 m.

The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale? 1 cm x m 4 cm 12 m Set up proportion using scale length . actual length = 1  12 = x  4 Find the cross products. 12 = 4x 3 = x Divide both sides by 4. The scale is 1 cm:3 m.