Lesson: Volume and Surface Area

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A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

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?
gmat-admin's picture

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...


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
gmat-admin's picture

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.


Hi Brent, in the context of the below question can there be a general statement that says if any container (cylinder, cube, rectangle) is half filled with water, the volume will remain the same if the same shape is rotated to the other side? (https://gmatclub.com/forum/a-closed-cylindrical-tank-contains-36pi-cubic-feet-of-water-134500.html)

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?
gmat-admin's picture

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.


Hi Brent, can the below question be solved using the concept of surface area? Surface area of container - surface area of cylinder = surface area of water with new height?


gmat-admin's picture

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?


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