The document discusses how scale factors relate the measurements of similar shapes that are enlarged or reduced versions of one another. It provides examples of finding surface areas and volumes of cubes, spheres, cylinders, and prisms when given the scale factor between the original and enlarged shapes. Scale factors of area are the square of the scale factor of length, and scale factors of volume are the cube of the scale factor of length.

2. Similar shapes

3. 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))

4. 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

5. 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

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

7. 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