656 Measurement and Proportional ReasoningVolume of Similar Solids
A triangular prism has a volume of 432 cubic yards. If the prism
is reduced to one third its original size, what is the volume of the
new prism?
V = 432 × ( _^1
3(^) )
3
Multiply by the cube of the scale factor.
V = 432 × ^1
27
Cube ^13.
V = 16 yd^3 Simplify.
The volume of the new prism is 16 cubic yards.
c. A square pyramid has a volume of 512 cubic centimeters. What
is the volume of a square pyramid with dimensions one fourth
of the original?
HOCKEY The standard hockey puck
measures as shown at the right. Find
1 in.
1.5 in.
the surface area and volume of the
giant puck at the left. Use 3.14 for π.
Find the volume and surface area
of the standard puck first.
V = πr^2 h S.A. = 2 (πr^2 ) + 2 πrh
≈ (3.14)(1.5)^2 (1) ≈ 2(3.14)(1.5)^2 + 2(3.14)(1.5)(1)
≈ 7.065 in^3 ≈ 14.13 + 9.42
≈ 23.55 in^2
Find the volume and surface area of the giant puck using the
scale factor.
V = V(40)^3 S.A. = S.A.(40)^2
= (7.065)(40)^3 = (23.55)(40)^2
= 452,160 in^3 = 37,680 in^2
The giant hockey puck has a volume of 452,160 cubic inches and a
surface area of 37,680 square inches.
d. ERASERS The dimensions of a rectangular eraser are 2.4 inches
by 4.6 inches by 1 inch. Find the surface area and volume of a
similar eraser that is 5 times as large.
Real-World Link
The hockey puck that
appears to be
crashing into the
side of the wall at
Nationwide Arena
in Columbus, Ohio, is
about 40 times
the actual size of a
standard puck.
RR
T
652_659_C11_L2_895130.indd 656 12/30/09 4:39 PM