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Similar shapes. 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. V A =xyz. V B =kxkykz=k 3 (xyz). S A =2(xy+xz+yz). S B =2(kxky+kxkz+kykz)

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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))



Sphere m is enlarged with scale factor 5 to obtain n find the volume of n
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
Cylinders G and H are similar.Find the radius of H

SG=14πcm2

SG=224πcm2

G

rG

H

rG=1.5cm

k2 = 224π/14π= 16

so k=4

and rH= 4x1.5 = 6cm


Prisms p and q are similar find the surface area of p
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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