IXL | Volume and surface area of similar solids

The figures below are similar.

4 mm

5 mm

S1 = ?

S2 = 100 mm2

What is the surface area of the smaller rectangular prism?

S1 = square millimeters

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question

The figures below are similar.

3 cm

9 cm

S1 = ?

S2 = 1,296 cm2

What is the surface area of the smaller rectangular prism?

S1 = square centimeters

key idea

The following proportion applies to similar solids:

where
a
b
is
the
ratio
of
the
corresponding
dimensions,
and
S1
S2
is
the
ratio
of
the
surface
areas.

solution

Find the square of the ratio of the corresponding dimensions:

Find the ratio of the surface areas:

1,296

Use these two ratios to set up a proportion and solve for S1.

1,296

(

1,296

)

1,296

(

1,296

)

Multiply both sides by 9 · 1,296

1,296

Simplify

1,296

Simplify

1,296

Divide both sides by 9

144

The surface area of the smaller rectangular prism is 144 square centimeters.

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U.4Similar solids

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