A rectangular tank 10 inches by 8 inches by 4 inches is filled with water. If…
2024
A rectangular tank 10 inches by 8 inches by 4 inches is filled with water. If all of the water is transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smaller tanks are needed?
- A.
9
- B.
12
- C.
16
- D.
21
Show answer & explanation
Correct answer: B
Concept
To find how many identical containers of a smaller volume are needed to hold a total volume of liquid, divide the total volume by one container's volume and round the result UP to the next whole number — a fractional container can never hold the leftover liquid, so any remainder still needs one more full tank.
Application
Volume of the rectangular tank = length × width × height = 10 × 8 × 4 = 320 cubic inches.
Volume of one cube-shaped tank = side × side × side = 3 × 3 × 3 = 27 cubic inches.
Number of tanks required = total volume ÷ volume of one tank = 320 ÷ 27 ≈ 11.85.
Since 11 tanks would hold only 11 × 27 = 297 cubic inches, which is less than 320, round up to 12 tanks.
Cross-check
12 tanks hold 12 × 27 = 324 cubic inches, enough to contain all 320 cubic inches of water, while 11 tanks (297 cubic inches) fall short — confirming 12 is the smallest number of tanks that works.
12 tanks are needed in total.