SIMILAR SHAPES

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
VA=xyz
SA=2(xy+xz+yz)
Write down expressions for the surface area & volume of A
VB=kxkykz=k3(xyz)
SB=2(kxky+kxkz+kykz)
=k2(2(xy+xz+yz))
Scale, area & volume factors
Sphere M is enlarged with scale factor 5 to obtain N.
Find the volume of N
M
N
VM=20cm3
VN=53x20=2500cm3
Cylinders G and H are similar.
Find the radius of H
SG=14πcm2
SG=224πcm2
G
H
rG
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
VP=15cm3
VQ=405cm3
SQ=162cm2
P
Q
k3 = 405/15 = 27
so k=3 and k2=9
and SP= 162 / 9 = 18cm2
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