A right circular cylinder has a height of 20 and a radius of 5. A rect

Question

A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?

A. 500(π – 3)
B. 500(π – 2.5)
C. 500(π – 2)
D. 500(π – 1.5)
E. 500(π – 1)

Show Answer

Official Answer

D

A. 500(π – 3) 
B. 500(π – 2.5) 
C. 500(π – 2) 
D. 500(π – 1.5) 
E. 500(π – 1)

anirbanroy · Answer

D
Volume of cylinder = pie*r^2*h = 500pie
Now, base of the inner solid is a square.
Since all the corners of the quadrilateral touch the circle, length of diagonals is the diameter which is 10.
Therefore area of the square = 1/2*(diagonal)^2 = 50
Now volume of any regular pyramid id (are of base)*height
Therefore, are of the inner solid is 50*15 = 750

The available volume is 500*pie - 750 = 500(pie - 1.5)

peachfuzz · Answer

A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?

A. 500(π – 3)
B. 500(π – 2.5)
C. 500(π – 2)
D. 500(π – 1.5)
E. 500(π – 1)

Show Answer

Official Answer

D

The square base has sides of sqrt(50) due to the 45-45-90 triangle

20*25*pi - 15*sqrt(50)^2
=500(π – 1.5)

D. 500(π – 1.5)

Fdambro294 · Answer

Start with the Bottom Face of the Rectangular Solid that is a Square. Since Each of the Corners of the Solid is Tangent to the Cylinder, the Bottom Face Square of the Rect. Solid will be INSCRIBED Inside the Circle on the Bottom of the Cylinder.

Rule: when a Square is Inscribed Inside a Circle, the Diameter of the Circle = Diagonal of the Square

Diagonal of a Square = (Side of Square = s) * sqrt(2)

Diameter of Circle on Bottom of Cylinder = 2 * 5 = 10

(s) * sqrt(2) = 10

(s) = (10) / (sqrt(2))

The Dimension of the Rectangular Solid are:

10 / sqrt(2)

and

15

To Find the Volume of the Liquid that fills the Cylinder AROUND the Inserted Rect. Solid, we need to find:

(Volume of Cylinder) - (Volume of Rectangular Solid) =

- (L * W * H) =

- ( 10/sqrt(2) * 10/sqrt(2) * 15) =

500(pi) - ( 10 * 10 * 15 / (sqrt(2))^2 ) =

500(pi) - (1,500 / 2) =

500(pi) - 750 =

------taking 500 Common to match the Answer Choices-----

500(pi) - 750 = 500 * ( (pi) - 750/500) = 500 * ( (pi) * 3/2 ) =

500 * ( (pi) - 1.5)

-D-

baraa900 · Answer

can you explain this part? ------taking 500 Common to match the Answer Choices-----

500(pi) - 750 = 500 * ( (pi) - 750/500) = 500 * ( (pi) * 3/2 ) =

500 * ( (pi) - 1.5)

Fdambro294 · Answer

Sure

Think of it like this. If you had to Multiply the 500 we factored out, what would you need to multiply it by to get back to the Original 750?

500 * (1.5) = 750

Thus, when you factor out the 500, think of it as leaving 1.5 in its place

Just like if you had:

2x + 6

2 * (x + 3)

After factoring out the 2, you had to leave 3 in its place. If you were to multiply 2 back through the parenthesis again, you would end up with:

2x + 6 again

Does that make sense?

In hindsight, I should have just left the 1.5 behind instead of 750/500, but I take my “steps” to the extreme sometimes lol

There are times when you find an answer and you need to make it match the answer choices. This was one of those times.

And even though the percentage seems high for a “hard” question, this was a very difficult question.

Posted from my mobile device

CEdward · Answer

Just wondering here if GMAT ever throws in  unnecessary details . I can't say I've seen many questions that do include such details.

This one here...the volume is completely irrelevant. The question amounts to asking what's the difference b/w the area of the cylinder and box.

Paras96 · Answer

A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?

A. 500(π – 3)
B. 500(π – 2.5)
C. 500(π – 2)
D. 500(π – 1.5)
E. 500(π – 1)

Show Answer

Official Answer

D

SOLUTION: The diagonal of the square base will be equal to the diameter of the cylinder in which it is placed = 10
diagonal of square =  a,
where a is the side of the square base
=> a=10
=>a=10/ 
=>Volume of rectangular solid = l*(square base side)^2 
=>15*(a)^2 = 15(10/root2)^2 =15*(100/2)=750
volume of cylinder will be- pi   h = pi*25*20=500pi
the volume of liquid will be = volume of cylinder-volume of rectangular solid
 = 500pi-750
 = 500(pi-750/500) 
 = 500(pi-3/2) => 500(pi-1.5)

Hence answer D

A right circular cylinder has a height of 20 and a radius of 5. A rect

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A right circular cylinder has a height of 20 and a radius of 5. A rect

Prep Toolkit

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