# Math

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The surface area of a rectangular prism is 10.4 in2. What is the surface area of a similar prism that is larger by a scale factor of 3?

• Math -

The surface areas of similar solids is proportional to the square of their sides
since the ratio of sides is 1 : 3
their surface areas have the ratio 1^2 : 3^2 or 1 : 9
so the surface area is 9(10.4) or 93.6

or

original width = x
original length = y
original heigt = z
original surface area = 2(xy) + 2(xz) + 2(yz)
= 2(xy + xz + yz)

new width = 3x
new length = 3y
new height = 3z
new surface area = 2(9xy) + 2(9xz) + 2(9yz)
= 18(xy + xz + yz)

ratio of new to old = 18(xy + xz + yz) : 2(xy + xz + yz)
= 9 : 1

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