SAT Math Multiple Choice Practice Question 195: Answer and Explanation
This rectangular box, which is empty, has a square base with a length of 5 inches and a height of 8 inches. Beginning at 3 p.m., sand is poured into it at a rate of 5 cubic inches per minute. At what time will the box be exactly three-quarters full?
A. 3:06 p.m.
B. 3:25 p.m.
C. 3:30 p.m.
D. 3:35 p.m.
E. 3:42 p.m.
Correct Answer: C
C. If you want to fill the box three-quarters full, you need to determine what three quarters of the volume of the box is: 3/4(5 × 5 × 8) = 3/4(200) = 150 in3. If 5 cubic inches of the box are filled per minute, it will take 150/5 = 30 minutes for the box to fill three quarters of the way from empty. If it starts to fill at 3 p.m., then at 3:30 p.m., it will be three-quarters full. Choice (C) is the right time.