Understanding Similar Shapes and Enlargement in Geometry
Explore the concepts of similar shapes, enlargement, surface area, and volume in geometry with detailed expressions and examples. Discover how scale factors affect the size and dimensions of geometric figures through practical applications. Enhance your knowledge of geometric properties and their transformations.
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Presentation Transcript
Cuboid A is enlarged with scale factor k to obtain B. Find expressions for the surface area & volume of B Write down expressions for the surface area & volume of A x A B z y VA=xyz VB=kxkykz=k3(xyz) SA=2(xy+xz+yz) SB=2(kxky+kxkz+kykz) =k2(2(xy+xz+yz))
Scale, area & volume factors If A is enlarged by scale factor k to give B, then: Name Notation Scale factor k kLA=LB Area factor k2 k2SA=SB Volume factor k3 k3VA=VB
Sphere M is enlarged with scale factor 5 to obtain N. Find the volume of N N M VM=20cm3 VN=53x20=2500cm3
Cylinders G and H are similar. Find the radius of H SG=14 cm2 SG=224 cm2 G rG H rG=1.5cm k2 = 224 /14 = 16 so k=4 and rH= 4x1.5 = 6cm
Prisms P and Q are similar. Find the surface area of P VP=15cm3 VQ=405cm3 P Q k3 = 405/15 = 27 so k=3 and k2=9 and SP= 162 / 9 = 18cm2 SQ=162cm2
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