IXL - Surface area and volume of similar solids II (Geometry practice)

The figures below are similar. The volume of each figure is given.

V1 = 27 cm3

V2 = 8 cm3

What is the ratio of the height of the larger rectangular pyramid to the height of the smaller rectangular pyramid?

Write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

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question

The figures below are similar. The surface area of each figure is given.


S1 = 225 mm2	S2 = 2,025 mm2

What is the ratio of the length of the smaller rectangular prism to the length of the larger rectangular prism?

Write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

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:

225

2,025

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

Take the square root of both sides

Write the fraction as a ratio.

→

1:3

The ratio of the length of the smaller rectangular prism to the length of the larger rectangular prism is 1:3.

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Surface area and volume of similar solids I

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