GRE Quant part Geometry (25 exercises)

[Maha]

I am preparing to sit for the GRE exam and studying on my own. I have a few questions regarding the maths part.
From Solid figures:
1) The volume of a box with a square base is 128cc. The height of the box is twice the breadth of the box.Find the height.
My solve- V=128, since it's given, square box so a³= 128, a=5 & h=2w (w=width/breadth;h=height) and since square box so w=5 then h=2x5=10
Not sure if it's correct, my procedure I mean & I don't have any answer sheet here.

2) Three cylindrical tanks of diameters 2m,4m,8m & of same height are to be filled simultaneously. What is the ratio of time taken in which they are filled?
My solve: V=rate x time
v₁:v₂:v₃
cylinder volume= pi x r² xH
pi and h cuts all through & am left with 1:4:16. Want to know if it's correct way.

Haven't attempted the following qs because I couldn't figure out how to start-

3) The radius of a right circular cylinder is increased by 40%. find the percentage increase in volume.
4) Find the volume of the largest circular cone that can be cut out of a cube of side 6m?
5) The diameter of the circular building is 14m, which is 33m in height. The staircase has been built along the curved surface in such way that the first step & last step are in vertical line. Find the length of the staircase.
6) What is the length of the wire of diameter 0.4m made out of solid sphere of radius 6m.

Now onto co ordinate geometry- attaching photos, the image is inverted can't make it straight & problem with no.3

need help with no.6
need help with 11,13,14,15
help with no.1

 

[Deleted member 4993]

I am preparing to sit for the GRE exam and studying on my own. I have a few questions regarding the maths part.
From Solid figures:
1) The volume of a box with a square base is 128cc. The height of the box is twice the breadth of the box.Find the height.
My solve- V=128, since it's given, square box so a³= 128 (incorrect), a=5 & h=2w (w=width/breadth;h=height) and since square box so w=5 then h=2x5=10
Not sure if it's correct, my procedure I mean & I don't have any answer sheet here.

V = a² * h = a² * (2a) = 2a³ = 128

2a³​ = 128 →

a³​ = 64

continue.....

 

[Maha]

Some more problems

Thank you Subhotosh Khan. Would really appreciate it if you or any other member could help me out with the rest.
I can't make the images straight, I took the photos properly but while uploading here it comes like this. If the image is saved & then viewed, I think it'll be alright.

no.7
no.10
no.17
no.34
no.32
no. 34
no. 12
no. 14
no. 27
no. 29

 

[Maha]

More Problems

The images become inverted when uploading here and I can't fix it. I think when the images are saved and viewed, it'll be alright. Thanks in advance
no. 35 here there's a comparison, which one is bigger, column a or b
no. 38

 

[mmm4444bot]

I can't make the images straight …

You can, if you access image software (like MS Paint) that rotates images.

I took the photos properly but while uploading here [they turn upside down] …

The server does not alter the orientation of image files. The images appear upside down because your device was upside down, when you captured the pictures. (If they appear rightside up on your device's screen, then you're holding the device upside down!)

… If the image is saved & then viewed, I think it'll be alright.

This is not correct. Every image file has an orientation. If you create an upside down image, it will always appear upside down (until edited).

It's really not up to members to fix this issue for themselves. Your responsibility is to ensure that images appear correctly before submitting your posts. (This is why the forum software provides a preview button, so you can see how your submission will appear before posting it.)

Also, have you read the forum guidelines, yet? (You agreed to these guidelines, when you joined the forum.) We prefer separate threads for separate exercises. When a member starts a discussion regarding more than a dozen exercises in a single thread, the thread can become composed of 50 or more posts, over time. That's a nuisance which can lead to errors, for anyone trying to follow the discussion of a particular exercise.

 

[mmm4444bot]

3) The radius of a right circular cylinder is increased by 40%. find the percentage increase in volume.

The formula for percent change is:

(NewAmount - OriginalAmount) / OriginalAmount

As you were not given the value of the original radius or height, you will need to work symbolically.

Let h = the height of each cylinder

Let r = the radius of the original cylinder

Use symbol r to express the radius of the new cylinder.

Then, use the formula for the volume of a right cylinder to determine an expression for each of the volumes. Put those expressions into the formula above for percent change. Simplify, and you'll see symbols r, h, and Pi cancel, leaving you with the decimal form of the requested percent.:cool:

 

[mmm4444bot]

4) Find the volume of the largest circular cone that can be cut out of a cube of side 6m[.]

The base of a cube is a square.

The base of your cone is a circle.

What is the radius of the largest circle that will fit inside a square measuring 6 by 6 meters?

What is the height of the tallest cone that will fit inside a cube measuring 6 by 6 by 6 meters?

Once you know the radius and height, use the volume formula. :cool:

 

[mmm4444bot]

5) The diameter of the circular building is 14m, which is 33m in height. The staircase has been built along the curved surface in such way that the first step & last step are in vertical line. Find the length of the staircase.

This question could be better-worded.

I'm thinking that the building is a cylinder resting on its circular base, and that the staircase winds it's way around the inside wall forming a spiral whose ends are located at each end of a vertical line running from the base to the roof.

I think the length of the staircase depends upon the number of loops in the staircase, and the number of loops depends upon the height of each step.

The given information doesn't state the step height, so there must be a different interpretation of the exercise. I can't think of a different scenario; perhaps someone else here will.

Aha. After considering the ratio of the height to the diameter, I realized that this is a somewhat "squat" building. Now I'm thinking that we must assume the spiral staircase makes only one loop.

Try to visualize what the spiral would look like, if we were to replace the staircase with a curved line and then "unrolled" the cylindrical wall so that it laid flat. What shape would this flat wall have? What would the spiral line look like now?

If you have trouble visualizing this mentally, then take a sheet of typing paper, roll it into a cylinder, and tape it. Then, use a felt pen, and carefully draw a spiral around the outside of the cylinder. Start at one end of the seam, and end at the other end of the seam. It may take a few tries, until you get a fairly nice spiral that makes only one loop.

Once you have drawn a good representation (one loop), unroll the paper and look at the line. This ought to give you an idea about how to answer the question :cool:

 

[mmm4444bot]

6) What is the length of the wire of diameter 0.4m made out of solid sphere of radius 6m[?]

What is the volume of a solid sphere with radius 6 meters? That's the volume of the wire, too.

Think of the wire as a very long cylinder. Use the volume formula for a cylinder (where h represents the wire's length).

Substitute the known values, in this formula, and solve for h. :cool:

 

[Steven G]

I am preparing to sit for the GRE exam and studying on my own. I have a few questions regarding the maths part.
From Solid figures:
1) The volume of a box with a square base is 128cc. The height of the box is twice the breadth of the box.Find the height.
My solve- V=128, since it's given, square box so a³= 128, a=5 & h=2w (w=width/breadth;h=height) and since square box so w=5 then h=2x5=10
Not sure if it's correct, my procedure I mean & I don't have any answer sheet here.

Just because the base (the bottom say) is a square does not mean the figure is a cube!

You say that a^3 is 128 which means that ALL the dimensions are the same. 5^3 is not 128. WHEN YOU MULTIPLY INTEGERS THAT INCLUDE A 5 THAT PRODUCT WILL END IN A 5 OR 0. YOU KNOW THAT!!!!

Let's assume that 5^3 is 128 for a moment. But now you say that the 3rd dimension h is 10. Well 5*5*10 is not 128, but rather 5*5*5 is 128 (actually it is 125)