Volume of a prism

Question

The base of a prism is equilateral with 6 cm sides, and the figure's height is perpendicular to its base. The figure is one-third full of water. The water is completely transferred into six identical cubes with 3cm sides. Each is completely full. What is the height of the now-empty prism?

I calculated the volume of the cubes: 3^3=27 27*6=162

I calculated the area of the triangle: ((√3)*6^2))/4=9√3

The volume of the prism is: 9√3*height

You know that 162 is 1/3 the volume of the prism so 486 is the total volume of the prism.

So 486=9√3*height so 486/9√3= height

How do I get the answer 18√3??

I think I have to do something with the 27*6 which is 3^3*6 but I just don't see it, can someone please help me?

dabral · Answer

Lars1988

The GMAT does not test you on volume of prisms. If they do, they will give you the formula for the volume. I know they have asked questions dealing with surface area and volume of spheres, but they gave the expressions for those quantities in terms of the radius.

The above question does not fit GMAT guidelines, and I would personally ignore this question.

Dabral

Lars1988 · Answer

The GMAT does not test you on volume of prisms. If they do, they will give you the formula for the volume. I know they have asked questions dealing with surface area and volume of spheres, but they gave the expressions for those quantities in terms of the radius.

The above question does not fit GMAT guidelines, and I would personally ignore this question.

Dabral

But this question comes straight out of the gmat prep material, so I think I can get a question like this at the test. The question can be solved I just do not know how, I know the answer is 18√3 but do not know how to get to this answer.

dabral · Answer

Are you saying that this from an official GMAT source? In that case I would like to know the exact reference or a screen capture.

If this from a GMAT book written by some random test prep company, then that is a different story.

Dabral

Lars1988 · Answer

If this from a GMAT book written by some random test prep company, then that is a different story.

Dabral

Oke yes is from GmatAmsterdam, the question they ask are coming straight out of the gmat prep. guide. Maybe this question is just for teaching about this specific subject. But it is very gmat like, especially the calculation 3*3^3*6=9√3*h. So if it is possible could you still give me the answer?

dabral · Answer

The question is poorly written and as far as I can tell is incomplete, so I can't help. My personal advice is that you should not waste your valuable time on poorly written unofficial GMAT questions. Stick to official GMAT questions as much as you can.

Dabral

Dabral

Lars1988 · Answer

Well, I see that I made a mistake in asking the question, I told you this was the question: The base of a prism is equilateral with 6 cm sides, and the figure's height is perpendicular to its base. The figure is one-third full of water. The water is completely transferred into six identical cubes with 3cm sides. Each is completely full. What is the height of the now-empty prism?

But it supposed to be: The base of a prism is an equilateral   triangle   with 6 cm sides, and the figure's height is perpendicular to its base. The figure is one-third full of water. The water is completely transferred into six identical cubes with 3cm sides. Each is completely full. What is the height of the now-empty prism?

Now you have got all the information you need to solve this question because you know what kind of prism it is and the formulas you should know by heart, cause in the other gmat questions from the official guide they won't give you a formula for the volume either. Apart from that an equation like: 3*3^3*6=9√3*h where you need to solve for h, is a very gmat like question. So I still like to know how to solve this equation so that is becomes 18√9. Could you please help me?

Lars1988 · Answer

Can someone please help me? I really want to know how the calculation is made.

KarishmaB · Answer

The base of a prism is an equilateral triangle with 6 cm sides, and the figure's height is perpendicular to its base. The figure is one-third full of water. The water is completely transferred into six identical cubes with 3cm sides. Each is completely full. What is the height of the now-empty prism?

Volume of the prism = Area of equilateral triangle * Height of prism

Volume of water in the prism = Area of base * (1/3)Height  = \frac{\sqrt{3}*6^2}{4} * \frac{1}{3} * Height

Volume of a cube = side^3

Volume of water in all 6 cubes  = 6 * 3^3  (since the cubes are full of water, volume of cube = volume of water)

6 * 3^3 = \frac{\sqrt{3}*6^2}{4} * \frac{1}{3} * Height

\frac{4*3^4}{6*\sqrt{3}} = Height of cylinder

Height of cylinder = 18\sqrt{3}

Note: Just like you can visualize a cylinder as cut outs of circle stacked together to give it height, you can visualize a prism as cut outs of equilateral triangles stacked together to give it height. In such cases, volume of the solid = Area of base * Height.
Check out our geometry book for a discussion on common 3D shapes.

Volume of a prism

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