Areas & Volumes of Similar Solids Objective: 1) To find relationships between the ratios of the areas & volumes of similar solids.

Similar Solids Similar Solids – Have the same shape, & all their corresponding dimensions are proportional. –Proportional – Equal Ratios 10in 15in 4in 6in Heights must be proportional! Radii must be proportional!

Ex.1: Are the following pairs of solids proportional?? No! –Not the same shape. Yes –2x as big or ½ as large. 4cm 2ft 8ft 1ft 4ft 1 2 = 1 2 = 4 8

Th (10-12) If side (similarity) ratio is a:b, then 1)Ratio of their corresponding areas a 2 :b 2. 2) Ratio of their volumes is a 3 :b 3.

Ex.2: Surface area ratio Find the side (similarity) ratio of two similar cylinders with surface areas of 98ft 2 & 2ft 2. –Write areas as a ratio. –Reduce –√–√–√–√ 98ft 2 2ft 2 = 49ft 2 1ft 2 = 7ft 1ft ** The height of the large cylinder is 7x bigger than the smaller cylinder. ** The radius of the large cylinder is 7x bigger than the smaller cylinder.

Ex.3: Volume Ratio Two similar square pyramids have volumes of 48cm 3 & 162cm 3. The surface area of the larger pyramid is 135cm 2. Find the surface of the smaller pyramid. –First find the side ratio. Write the volumes as a ratio. Reduce 3√3√3√3√ –Set up a surface area ratio 48cm 3 162cm 3 = 8cm 3 27cm 3 = 3 √ 8ft 3 3 √ 27ft 3 = 2cm 3cm = x = x x = 60cm 2

What have we learned?? In order for two solids to be similar they must be –The same shape –Corresponding parts have to be proportional If the side ratio is a:b, then –Area ratio is a 2 :b 2 –Volume ratio is a 3 :b 3