Surface Area and
Volume of Similar
Figures
Section 12.7
Definition
O A polyhedron is a solid that is bounded by
polygons.
Tell whether each figure
below is a polyhedron.
Definition
O Two solids of the same type with equal ratios
of corresponding linear measures, such as
heights or radii, are called similar solids.
Tell whether each given right
rectangular prism is similar to the right
rectangular prism shown below.
Similar Solids Theorem
O If two similar solids have a scale factor of a :
b, then corresponding areas (and surface
areas) have a ratio of a2 : b2 and
corresponding volumes have a ratio of
a3 : b3.
The pyramids are similar. Pyramid P has a volume of
1000 cubic inches and Pyramid Q has a volume of 216
cubic inches. Find the scales factor of Pyramid P to
Pyramid Q.
Solid I is similar to Solid II. Find
the scale factor of Solid I to Solid II.
Practice
O p.850: 3-7, 12-15