IXL | Volume and surface area of similar solids

The figures below are similar.

3 in

9 in

S1 = 225 in2

S2 = ?

What is the surface area of the larger rectangular prism?

S2 = square inches

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Learn with an example

question

The figures below are similar.

1 yd

2 yd

S1 = ?

S2 = 256 yd2

What is the surface area of the smaller rectangular prism?

S1 = square yards

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:

256

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

256

(

256

)

256

(

256

)

Multiply both sides by 4 · 256

256

Simplify

256

Simplify

256

Divide both sides by 4

The surface area of the smaller rectangular prism is 64 square yards.

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U.4Similar solids

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