8.4 Volume and Areas of Similar Figures Geometry Topic/Objective: To find the volume and surface area of similar figures. EQ: How do you find the surface area and volume of similar figures?

8.4 volume and Areas of Similar Figures Is this statement True or False? The picture is twice as big as our smaller TV. Screen Size: 6  9 Screen Size: 12  18 Area: 54 Area: 216 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Problem Draw a rectangle that measures 3  2. 6 The area is ? Double the lengths of the sides and draw a rectangle that measures 6  4. The area is ? 24 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Example continued When the lengths of the sides were doubled, did the area double? NO! 6 24 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures So what happened? 3 The ratio of the sides: 6 2 ? The ratio of the areas: 6 ? 24 4 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Notice: 3 The ratio of the sides: 6 2 The ratio of the areas: 6 24 4 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Example 2 These figures are similar. The area of the smaller one is 20. Find the area of the larger figure. 4 Ratio of the sides: Ratio of their areas: 10 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Example 2 continued Write the proportion and solve: 20 125 x 4 10 Ratio of sides 2:5 Ratio of areas 4:25 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Problem If the figures are similar, what is the length of the side marked x? 4 A = 36 x A = 100 Remember: the ratio of the areas is the square of the ratios of the sides. Or, the ratio of the sides is the square root of the ratios of the areas. 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Problem Solution 4 A = 36 x A = 100 The ratio of the sides is the square root of the ratios of the areas. 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Volume and Surface area of similar solids. 8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures The ratio of sides cubed gives us the ratio of volume. Side length is doubled: Scale factor is 2   tells us the scale factor of volume.     8.4 volume and Areas of Similar Figures

8.4 volume and Areas of Similar Figures Summary: The scale factor of all areas of similar figures and solids is the scale factor of sides squared. The scale factor of all volumes of similar solids is the scale factor of sides cubed. 8.4 volume and Areas of Similar Figures