- The length, width, and height of a rectangular
box, in centimeters, are a, b,andc,wherea, b,
andcare all integers. The total surface area of
the box, in square centimeters, is s,and the
volume of the box, in cubic centimeters, is v.
Which of the following must be true?
I. vis an integer.
II. sis an even integer.
III. The greatest distance between any two
vertices of the box is.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III - The figure above shows a rectangular box in
which AB= 6, AC= 5, AD= 8, and F is the
midpoint of BE. What is the length of the short-
est path fromA toF that travels only on the
edges of the box and does notpass through ei-
ther pointBor pointC?
(A) 27.5
(B) 28.5
(C) 29.5
(D) 30
(E) 30.5
A
B
C
F
E
D
abc^222 ++- A pool-filling service charges $2.00 per cubic
meter of water for the first 300 cubic meters
and $1.50 per cubic meter of water after that.
At this rate, how much would it cost to have
the service fill a rectangular pool of uniform
depth that is 2 meters deep, 20 meters long,
and 15 meters wide?
(A) $450
(B) $650
(C) $800
(D) $1,050
(E) $1,200 - In the figure above, a rectangular box has the
dimensions shown. Nis a vertex of the box,
andMis the midpoint of an edge of the box.
What is the length of NM
–––
?
(A)
(B)
(C)
(D)
(E)^125
108
98
77
63
M
N
5
6
8
SAT Practice 7: Volumes and 3-D Geometry
396 McGRAW-HILL’S SAT