PQID – PS95602.01 | OGQR 2020: Question No. 96
When a rectangular vat that is 3 feet deep is filled to (2/3) of its capacity, it contains 60 gallons of water. If 7 1/2 gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Geometry |
| Sub-Topic | Rectangular Solids |
| Difficulty | Medium |
Solution
Given
In this question, we are given
- When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water.
- 7(Ā½) gallons of water occupies 1 cubic foot of space.
To Find
We need to determine
- The area, in square feet, of the base of the vat.
Approach & Working
When the vat is filled to 2/3 of its capacity, it contains 60 gallons of water.
- Hence, the capacity of the vat = 60 * 3/2 = 90 gallons
- The space occupied, when the vat is fully filled = 90/7.5 = 12 cubic feet
If the area of the base is n, then we can say
- Area of the base * height = volume (or space occupied)
Or, n * 3 = 12
Or, n = 4
Hence, the correct answer is option A.
Takeaways:
- If 2/3rd of something is āXā, then total of that = X * 3/2
- Volume = Area of base * height
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