Similar shapes

Cuboid A is enlarged with scale factor k to obtain B. Find expressions for the surface area & volume of B y x z A B V A =xyz S A =2(xy+xz+yz) Write down expressions for the surface area & volume of A V B =kxkykz=k 3 (xyz) S B =2(kxky+kxkz+kykz) =k 2 (2(xy+xz+yz))

Scale, area & volume factors NameNotation If A is enlarged by scale factor k to give B, then: Scale factor kkL A =L B Area factork2k2 k 2 S A =S B Volume factor k3k3 k 3 V A =V B

Sphere M is enlarged with scale factor 5 to obtain N. Find the volume of N M N V M =20cm 3 V N =5 3 x20=2500cm 3

Cylinders G and H are similar. Find the radius of H S G =14πcm 2 S G =224πcm 2 G H rGrG r G =1.5cm k 2 = 224π / 14π = 16 so k=4 and r H = 4x1.5 = 6cm

Prisms P and Q are similar. Find the surface area of P V P =15cm 3 V Q =405cm 3 S Q =162cm 2 P Q k 3 = 405 / 15 = 27 so k=3 and k 2 =9 and S P = 162 / 9 = 18cm 2

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