Surface Area of Similar Solids
The surface area of a rectangular prism is 78 square centimeters.
What is the surface area of a similar prism that is 3 times as large?
S.A. = 78 × 32 Multiply by the square of the scale factor.
S.A. = 78 × 9 Square 3.
S.A. = 702 cm^2 Simplify.MODELS Refer to the previous page. The surface area of the
exposed portion of the pyramid atop the Washington Monument
is 4,012 square feet. What is the surface area in square inches, to
the nearest tenth, of the pyramid on Stephen’s model?S.A. = 4,012 × (^) ( ^1
100
(^) )
2
Multiply by the square of the scale factor.
S.A. = 4,012 × ^1
10,000
Square _ 1001.
S.A. = 0.4012 ft^2 Simplify.
S.A. = 0.4012 ft · ft × _12 in.
1 ft
× 12 in.
1 ft
Convert to inches.
S.A. = 57.8 in^2 Simplify.
The surface area of Stephen’s model is 57.8 square inches.
a. The surface area of a triangular prism is 34 square inches. What
is the surface area of a similar prism that is twice as large?
b. RAISINS The world’s largest box of raisins has a surface area of
352 square feet. If a similar box is smaller than the largest box
by a scale factor of ^1
48
, what is its surface area?
Refer to the cubes on the previous page.
Volume of Small Cube Volume of Large Cube
V = 4 · 4 · 4 V = ( 2 · 4)( 2 · 4)( 2 · 4)
= 2 · 2 · 2 (4 · 4 · 4)
= 23 (4 · 4 · 4)
The volumes of similar solids are related by the cube of the
scale factor.
Volume of Similar Solids
If Solid X is similar to Solid Y by a scale factor, then the volume
of X is equal to the volume of Y times the cube of the scale
factor.
Real-World Link
It takes about
4 1 _ 2 pounds of
fresh grapes to
make one pound
of raisins.
RR
Lesson 2C Similar Solids 655
652_659_C11_L2_895130.indd 655 12/30/09 4:39 PM