Similar shapes

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

Scale, area & volume factors

Name Notation If A is enlarged by scale factor k to give B, then: Scale factor k kL A =L B Area factor k 2 k 2 S A =S B Volume factor k 3 k 3 V A =V B

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

Cylinders G and H are similar.

Find the radius of H S G =14 πcm 2 S G =224 πcm 2 G r G r G =1.5cm

k 2 = 224 π / 14 π = 16 so k=4 and r H = 4x1.5 =

6cm

H

Prisms P and Q are similar.

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

18cm 2

S Q =162cm 2

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