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Math Expert V
Joined: 02 Sep 2009
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When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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20 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:22) correct 33% (02:28) wrong based on 402 sessions

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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 $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION

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Senior Manager  G
Joined: 25 Feb 2019
Posts: 335
Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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9
1
IMO A

volume = area of base *height

let the area be A

then volume = A*3

now this is filled to 2/3 of its capacity

so volume of water = 2/3*(A*3)

now the volume of water = 60(15/2)= 8 cubic feet

so 2/3*(A*3)= 8

So A = 8/2 = 4

Posted from my mobile device
##### General Discussion
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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4
2
[quote="Bunuel"]When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

Here is my take ....

The question is asking,what is the area of the base of the vat= a*b (a=length; b=breath)

Let's say total capacity of the vat= x
2x/3= 60 gallon
x= 90 gallon (total capacity)

If 15/2g of water occupies 1 cubic foot of space
then, 90g of water will occupy= 90*2/15 = 12 cubic foot of space in the vat (Total volume)

We can also write:
a*b*c= 12 cubic foot (c=depth; C=3 feet)
a*b*3= 12
a*b= 4 (which is length * breath= area of the base)

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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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3
Let's assume V as the volume of our vat. 2/3*X=60 so we can find V=60*3/2=90.
Volume=width*length*height, width*length= area of our base and width*length*3=90 => width*length=90/3=30
Our answer is 30*2/15=4, which is A.
Intern  B
Joined: 01 Dec 2018
Posts: 43
Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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3
Unitary method can be applied to this :

If, 2/3 is 60 gallons then 3/3(1) = 90 gallons
As 1 cubic feet = 15/2 ,
12 cubic feet = 15/2*12 (multiplying both sides by 12)
12 cubic = 90 gallons (total volume)

total area = 3*X = 12
Therefore, x = 4
A
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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1
Bunuel wrote:
When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION

Since the vat is 3 feet deep and water is filled to 2/3 of its capacity, the water is ⅔ x 3 = 2 feet deep. In cubic feet, the water is 60/7.5 = 8 cubic feet in volume. Since the water is 2 feet deep, the base of the vat must be 8/2 = 4 square feet.

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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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1
dcummins wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION

Since the vat is 3 feet deep and water is filled to 2/3 of its capacity, the water is ⅔ x 3 = 2 feet deep. In cubic feet, the water is 60/7.5 = 8 cubic feet in volume. Since the water is 2 feet deep, the base of the vat must be 8/2 = 4 square feet.

Hey Scott,

I'm a bit unsure how you moved from cubic units to square units here

We are using the formula volume = base area x height, which can be applied to not just cubes or rectangular solids, but to any “right solid”, such as a cylinder or prism. In this formula, the volume is measured in cubic units (cubic feet in our example) and the base area is measured in square units (square feet in our example). All we did to find the base area was to divide the volume by height, which will give the result in square units. The only thing to be careful about is to have all the units agree; in other words, you can’t divide cubic feet by meters and expect any reasonable answer.
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# Scott Woodbury-Stewart

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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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total fill in feet ; 3*2/3 = 2feet
and 60 gallons in feet have 60*2/15 = 8 ft^3 of water
so base has 8ft^3/2feet = 4ft^2
IMO A

Bunuel wrote:
When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION
Senior Manager  G
Joined: 12 Sep 2017
Posts: 308
Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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Snezanelle wrote:
Let's assume V as the volume of our vat. 2/3*X=60 so we can find V=60*3/2=90.
Volume=width*length*height, width*length= area of our base and width*length*3=90 => width*length=90/3=30
Our answer is 30*2/15=4, which is A.

Hello! Snezanelle,

Where does the 15 comes from?

Kind regards!
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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Bunuel wrote:
When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION

Let x be the area sq. foot of base. Volume of the water= x*2 ....(Height of tank filled id 2 ft.)

Now form the proportion 15/2 : 1 :: 60 : 2x
x=4.
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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jfranciscocuencag wrote:
Snezanelle wrote:
Let's assume V as the volume of our vat. 2/3*X=60 so we can find V=60*3/2=90.
Volume=width*length*height, width*length= area of our base and width*length*3=90 => width*length=90/3=30
Our answer is 30*2/15=4, which is A.

Hello! Snezanelle,

Where does the 15 comes from?

Kind regards!

Hi,
15/2 = 7*(1/2), which is mentioned in the problem.
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When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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60 gallons = (60/7.5)= 8 feet
Total Volume= πr^2h
So, πr^2×(3)×(2/3)=8
πr^2=area of base= 4 sq feet.

Posted from my mobile device
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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if 2/3 capacity = 60 gallons then 2x/3 = 60 and the capacity = 90 gallons

volume = length*width*height
height here = depth and we know the volume = 90
l*w*3=90
lw=30 gallons

Is there any legitimate way of using the volume to determine the base?
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Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap  [#permalink]

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ScottTargetTestPrep wrote:
Bunuel wrote:
When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If $$7\frac{1}{2}$$ gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

A.  4
B.  8
C.  12
D. 150
E. 225

PS95602.01
Quantitative Review 2020 NEW QUESTION

Since the vat is 3 feet deep and water is filled to 2/3 of its capacity, the water is ⅔ x 3 = 2 feet deep. In cubic feet, the water is 60/7.5 = 8 cubic feet in volume. Since the water is 2 feet deep, the base of the vat must be 8/2 = 4 square feet.

Hey Scott,

I'm a bit unsure how you moved from cubic units to square units here Re: When a rectangular vat that is 3 feet deep is filled to 2/3 of its cap   [#permalink] 12 Sep 2019, 17:55
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