SAT Math Multiple Choice Question 983: Answer and Explanation
The bottom of the fish tank shown is filled with rocks. The tank is then filled withwater to a height of 18 inches. When the rocks are removed, the height of the waterdrops to 16.5 inches. How many cubic inches of water do the rocks displace?
- A. 280
- B. 420
- C. 560
- D. 980
Correct Answer: B
Category: Additional Topics in Math / Geometry
Strategic Advice: Sometimes, it is necessary to think about a question logically before making any calculations. Here, the amount of water displaced is equal to the difference between the volume of water in the tank with the rocks and the volume of water in the tank without the rocks.
Getting to the Answer: You could find each of the volumes described. However, because the length and width of the tank do not change (only the height of the water changes), it would be quicker to find the difference in the heights of the water and find the volume of only that part of the water. The height of the water with the rocks is 18 inches and the height without the rocks is 16.5 inches, so 1.5 inches of water is displaced. Now, use the formula V = lwh to find that the amount of water displaced by the rocks is 28 × 10 × 1.5 = 420 cubic inches. This means (B) is correct.