Opener Find the volume of each figure. 2) 1) V = 267.95 cm 3 V ≈ 2,143,573 km 3 4 cm 80 km.

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Presentation transcript:

Opener Find the volume of each figure. 2) 1) V = cm 3 V ≈ 2,143,573 km 3 4 cm 80 km

Opener List the formula (from memory) for each: 1) Area of a rectangle 2) Area of a triangle 3) Area of a trapezoid 4) Area of a circle 5) Circumference of a circle 6) Volume of a prism 7) Volume of a cylinder 8) Volume of a pyramid 9) Volume of a cone 10) Volume of a sphere 11) Find the surface area and volume of the cylinder. SA = cm 2 12 cm 4 cm V = cm 3

□ I will be able to find measurements of similar solids. Objective

Vocabulary similar solids – two solids with equal ratios of all corresponding liner ( 1D ) measurements (like heights and radii) scale factor – the ratio of two similar solids Similar Not Similar

Units / Units 2 / Units 3 3 in 3 in 3 in 3 in 3 in 3 in Length = 3 in.Area = 9 in. 2 Volume = 27 in. 3 3 : 9 : 27 k : k 2 : k 3

Similar Solid Rules If two solids are similar with a scale factor of k, then the surface areas of the solids have a ratio of k 2. If two solids are similar with a scale factor of k, then the volumes of the solids have a ratio of k 3.

Ex 1 – Comparing Solids The two cylinders are similar. Their ratios of their surface areas is 4:9. Find the ratios of their heights and the ratios of their volumes. Let k be the scale factor. k 2 = 9 4 k = 3 2 Ratio of the heights: k = 3 2 Ratio of the volumes:k 3 = ft 3 ft

Ex 2 – Comparing Solids Name the scale factor of the two solids. Then determine the surface area and volume of the second solid. 2 in 8 in 2 in 2 in 8 in 8 in SA = 24 in 2 V = 8 in 3 SF = 8 2 = 4 SA = 4 2 = 16 24= 384 in 2 V = 4 3 = 64 8= 512 in 3

Homework WB 10.8 (#1-10)