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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? – OGQR 2020 Question #96 with Solution

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 1/2gallons 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  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.

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