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## Comment on

Volume and Surface Area## A rectangular box, with

A. 6

B. 12

C. 15

D. 30

E. 48

For this ques can we solve it by calculating the volume of the rectangular box divided by the surface area of each cans to get the no of cans?

## That strategy won't work,

That strategy won't work, since you're comparing surface areas and volumes, which are entirely different concepts.

Also, I should note that many students will want to find the volume of one can and then divide it into the total volume of the box. However, this strategy only works if we're pouring the liquid soup into the box.

If we're leaving the soup IN the cans, then we must consider the fact that there will be air pockets.

Here's my step-by-step solution: https://gmatclub.com/forum/a-rectangular-box-with-dimensions-of-12-inche...

Cheers,

Brent

## Hi Brent,

Can you please answer this question?

A thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?

(A) (15 - π)/2

(B) (5π)/4

(C) 15 - 2π

(D) 15 - π

(E) 2π

## Here are a few different

Here are a few different solutions: https://gmatclub.com/forum/as-shown-in-the-figure-above-a-thin-conveyor-...

Please let me know if you'd like me to elaborate on any of them.

Or I can provide a full solution if you wish.

Cheers,

Brent

## Hi Brent, in the context of

A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

## Question link: https:/

Question link: https://gmatclub.com/forum/a-closed-cylindrical-tank-contains-36pi-cubic...

If a container is half filled with water, then the volume of water will remain the same, regardless of how the container is positioned (as long as no water spills out).

Does that answer your question? I wasn't 100% sure what you were asking.

Cheers,

Brent

## Hi Brent, can the below

https://gmatclub.com/forum/a-solid-cylinder-with-radius-3-inches-sits-in-a-cylindrical-234443.html

## Question link: https:/

Question link: https://gmatclub.com/forum/a-solid-cylinder-with-radius-3-inches-sits-in...

It's not immediately clear to me how that strategy would work.

Can you show me some additional steps?

Cheers,

Brent

## Hi Brent,

I couldn't find any lesson on Rectangular Solids and how to calculate their Surface Area, Volume, etc. I was wondering if these are outside the scope of GMAT or whether I am missing something here.

Thanks & Regards,

Abhirup

## Hi Abhirup,

Hi Abhirup,

Those concepts are definitely tested on the GMAT, and the above video lesson covers those concepts.

Cheers,

Brent

## Hi Brent, facing difficulty

A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?

2

4

6

8

12

## To help you interpret the

To help you interpret the problem, here's a graphic showing 2 different ways a cylinder might be placed in a box: https://imgur.com/6SVrKIO

The question you've posted is basically a copy of an official GMAT question (except the dimensions are 6x8x10 instead of 4x8x12).

If you take a look at my full solution (https://gmatclub.com/forum/the-inside-dimensions-of-a-rectangular-wooden...) to that question, I'm pretty sure you'll be able to answer the question you posted.

Cheers,

Brent

## https://gmatclub.com/forum

The explanations mention that we need to know the dimensions of the carton for this to be sufficient. My question is, when do we require the need to use surface area as opposed to volume? If the surface were given instead of volume would that be different?

Fitting X objects into one big Y object seems to be quite common in DS problems.

## Question link: https:/

Question link: https://gmatclub.com/forum/what-is-the-number-of-cans-that-can-be-packed...

This isn't a very common question type. It's just that most test prep companies have created similar questions that are very similar to this Official Guide question.

I don't think I've ever seen a question of this nature (fitting cylinders into a box) where we are given the cylinder's surface area.

I wouldn't worry about that scenario.

Cheers,

Brent

## https://gmatclub.com/forum

I'm having trouble visualising these kind of questions. How do I determine which sides would allow me to fit the largest objects inside.

I came up with 160 pie with height of 10 and radius 4

## Question link: https:/

Question link: https://gmatclub.com/forum/what-is-the-volume-of-the-largest-cylinder-th...

You're right; these kinds of questions require the mental manipulation of various images.

In your solution, the height of the cylinder is 10.

This means, the flat part of the can is lying on the side with dimensions 6 x 8.

If the radius of the can is 4, then the DIAMETER is 8. Since the bottom of the box has dimensions 6 x 8, a can with diameter 8 won't fit in the box.

Cheers,

Brent

## https://gmatclub.com/forum

What if the dimensions in statement 1 were prime numbers? Would you be able to prove that its sufficient?

## Do you mean statement 1 is as

Do you mean statement 1 is as follows:

1) Two adjacent faces of the solid have areas 15 and 24, respectively AND the dimensions of the solid are prime numbers.

This scenario would create an impossible situation. If one side has an area of 24, then the two dimensions of that rectangle must have a product of 24.

However, there is no way to write 24 as the product of two prime numbers.

Cheers,

Brent

## No I meant to say that if we

1) Two adjacent faces of the solid have areas Prime Number X and Prime Number Y respectively.

## Do you mean for statement 1

Do you mean for statement 1 to NOT have any actual values?

Here are some possible re-wordings for statement 1:

1) Two adjacent faces of the solid have areas PRIME NUMBER X and PRIME NUMBER Y respectively.

This is definitely not sufficient (no values given)

1) Two adjacent faces of the solid have areas 7 and 11 respectively.

This is still not sufficient, since the dimensions COULD be 0.5 x 14 x 22, or they COULD be 1 x 7 x 11

1) Two adjacent faces of the solid have areas 7 and 11 respectively, AND each dimension is an INTEGER value.

SUFFICIENT. Here, the dimensions MUST be 1 x 7 x 11

Does that help?

Cheers,

Brent

## Yes that helps. Thanks.

## Hi Brent,

Could you provide your solution for this?

https://gmatclub.com/forum/a-tank-is-filled-with-gasoline-to-a-depth-of-exactly-2-feet-the-tank-202262.html

I have trouble understanding how statement 2 is sufficient.

Thanks for your help.

## Here's my solution: https:/

Here's my solution: https://gmatclub.com/forum/a-tank-is-filled-with-gasoline-to-a-depth-of-...

## Hi Brent,

https://gmatclub.com/forum/what-is-the-radius-of-the-largest-sphere-that-can-fit-into-a-box-of-di-275651.html

Can you explain how the answer still remains the same if the height is 12?

## Question link: https:/

Question link: https://gmatclub.com/forum/what-is-the-radius-of-the-largest-sphere-that...

The orientation of the box doesn't matter.

All that matters is that the maximum size of the sphere is restricted by shortest dimension of the box (in this case 8).

This means a sphere with radius 4 (i.e., diameter 8) will touch both sides of the box, which means a sphere with a radius greater than 4 will not fit in the box.

Does that help?

## Hi Brent, could you please

https://gmatclub.com/forum/a-square-wooden-plaque-has-a-square-brass-inlay-in-the-center-leaving-89215.html

My approach was:

Brass area = 25 = 5^2;

Total area = (5+2x)^2;

Wooden area = 39 = (5+2x)^2 - 25 => apply a^2-b^2 formula, simplify equation and plug in values. However, I couldn't get to the correct answer.

## We don't actually need to

We don't actually need to perform any calculations, as you will see in my solution: https://gmatclub.com/forum/a-square-wooden-plaque-has-a-square-brass-inl...

Here's an analogous question:

Joe has two trees in his backyard: A pine tree and a fir tree.

The ratio of the height of the pine tree to the height of the fir tree is 2 : 1.

Which of the following could be the height of the pine tree?

I. 8 meters

II. 10 meters

III. 45 meters

Answer: I, II and III

## Brent, is there a simpler way

https://gmatclub.com/forum/the-dimensions-of-a-ream-of-paper-are-8-1-2-inches-by-11-inches-by-294408.html

## I think this approach is

I think this approach is probably best: https://gmatclub.com/forum/the-dimensions-of-a-ream-of-paper-are-8-1-2-i...

I can't think of an easier/faster solution.

## https://gmatclub.com/forum

for this question, I got into the trap and chose C, but now I know what's going one.

## Question link: https:/

Question link: https://gmatclub.com/forum/how-many-books-will-fit-into-a-drawer-1-each-...

Good stuff.