SAT Subject Test Mathematics Level 2

Figure  4

Note:   Figure  not drawn   to  scale

Since the markers are too long to be turned horizontal, they must be gathered together vertically.
Put them in rows as long and wide as possible.

Since each marker has diameter 0.5", you can fit 12 across and 12 back, for a total of 144 markers.
Now all that remains is to find the volume of the markers and the volume of the box.

The volume of the box = 6 × 6 × 10 = 360.

The volume of one marker = πr^2 h = π(0.25)^2 × 9 ≈ 1.77.

The volume of all 144 markers ≈ 144 × 1.77 ≈ 254.88.

The volume unused is 360 – 254.88 ≈ 105.12.

The percent unused is , so the answer is (C).

Figure  4   shows   a   rectangular box and a   cylindrical marker, which   has diameter    0.5"    and height

9". If  the box is  filled  with    as  many    markers as  possible,   what    percentage  of  the space   will    be

unused?

1.

(A) 21.5%

(B) 24.6%

(C) 29.2%

(D) 31.8%

(E) 70.7%