If D represents the diameter of a cylinder and W represents the volume

Question

If D represents the diameter of a cylinder and W represents the volume of that cylinder divided by  π, (W=\frac{V}{π}) , which of the following could represent D and W of a cylinder for which the height equals the radius?

GmatTest2026 · Answer

Solution:

As we know Diameter = 2 Radius

W =  \frac{\pi*V(volume)}{\pi} (Given)

Volume of cylinder =  \pi*r^{2}*h

Height = Radius (Given)

So, we can put this above information and get W =  \frac{\pi* \pi*r^{2}*r}{\pi}---> W = r^{3}

Now. we look into the options D = 2 Radius(2*3=6)
 w =  r^{3} = 3^{3}  = 27

Gem165 · Answer

W = V/π = πr2h/π = r2h = r3(since height = radius is given)
so, W = r3. The only value which is a cube is 27 from the following options. And the corresponding radius becomes 3, so diameter, D becomes 2xr = 6.

Bismuth83 · Answer

1. The question asks us to  find a possible combination of the diameter and volume divided by  \pi  for a certain cylinder .

2. To do this, we need to connect these two values. The formula for volume in a cylinder is  V = \pi * r^2 * h .

3. Using the knowledge that the cylinder has an equal radius and height,  V = \pi * r^2 * h = \pi * r^3 \rightarrow W * \pi = \pi * (\frac{D}{2})^3 \rightarrow W = \frac{D^3}{8} .

4. Let's calculate W assuming D is one of the answer choices:

- D = 3.  W = \frac{3^3}{8} = 3.375 ,   which doesn't work  .
 - D = 6.  W = \frac{6^3}{8} = 27 ,   which works  .
 - D = 9.  W = \frac{9^3}{8} = 91.125 ,   which doesn't work  . 
 - D = 18, 27, and 36.   These won't work since W will be too big to be one of the answer choices  .

5. Our answer will be:   D - 6 and W - 27  .

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83676 Harsha GMAT-Club-Forum-iy5k0bjw.png

Usernamevisible · Answer

HarshavardhanR  - isn't this Geometry which is not there in the syllabus ?

HarshavardhanR · Answer

In general,

- Coordinate Geometry and Graphing of functions is very much part of the syllabus.
- Solid Geometry (cubes, cylinders, etc.) is  not officially a part  of the syllabus. 
- That said, I believe it is good to know just the very basic geometry concepts --- A quick revision of this is advisable as a safety precaution.
- Especially in DI, something basic, such as volume of cylinder or surface area of a cuboid, can still be tested, even if we may not see solid geometry questions in the Quant section. 
- Typically, I would expect the test-maker to provide us with any formulae we would need to apply. Still, just as a safeguard, learn the basic concepts - no need to sit and solve geometry sets for solid geometry.

Hope this helps.

If D represents the diameter of a cylinder and W represents the volume

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If D represents the diameter of a cylinder and W represents the volume

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