It is currently 21 Jan 2018, 22:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The inside dimensions of a rectangular wooden box are 6 inches by 8 in

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43349
The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

### Show Tags

04 Dec 2017, 21:57
Expert's post
3
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

19% (00:53) correct 81% (01:07) wrong based on 19 sessions

### HideShow timer Statistics

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
[Reveal] Spoiler: OA

_________________
Intern
Joined: 15 Oct 2017
Posts: 30
Location: Ireland
Concentration: Healthcare, Finance
The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

### Show Tags

04 Dec 2017, 23:31
Bunuel wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Let's assume that the bottom side of the box has dimensions 8*10 when the canister is placed in it. Obviously, the diameter can't be more than eight so the radius is 4 Height is 6
$$V = \pi * r^2 * h = 16\pi * 6 = 96\pi$$

Let's assume that the bottom side of the box has dimensions 8*6 when the canister is placed in it. Obviously, the diameter can't be more than 6 so the radius is 3 Height is 10
$$V = \pi * r^2 * h = 9\pi * 10 = 90\pi$$

Last edited by Vorovski on 05 Dec 2017, 08:17, edited 2 times in total.
Manager
Joined: 24 Nov 2016
Posts: 151
The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

### Show Tags

05 Dec 2017, 04:35
Bunuel wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Volume of a cylinder: $$pi*r^2*h$$
Radius = $$\frac{Diameter}{2}$$

The maximum diameter of a cylinder that fits inside the rectangular box is restricted to the length and width of the box.
So, if we have a length =8, width = 10 and height = 6, then max. diameter = 8 and radius = 4;
And, the volume of the cylinder: $$pi*4^2*6=pi*96$$

Let's try another, with length =8, width = 6 and height = 10, then max. diameter = 6 and radius = 3;
And, the volume of the cylinder: $$pi*3^2*10=pi*90$$

Largest radius we can have is 4.

Last edited by exc4libur on 07 Dec 2017, 15:41, edited 1 time in total.
Intern
Joined: 29 May 2012
Posts: 39
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

### Show Tags

05 Dec 2017, 06:34
1
KUDOS
exc4libur wrote:
Bunuel wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Volume of a cylinder: $$pi*r^2*h$$

Let's test the wooden box dimensions for the bottom and the height.
If we have a bottom of 6 and a height of 10 then the radius would be 3 and volume of cylinder = $$pi*3^2*10 = pi*90$$
If we have a bottom of 8 and a height of 10 then the radius would be 4 and volume of cylinder = $$pi*4^2*10 = pi*160$$
If we have a bottom of 10 and a height of 8 then the radius would be 5 and volume of cylinder = $$pi*5^2*8 = pi*200$$

So the maximum volume of the cylinder would be $$pi*200$$ with a radius of 5.

Might i check if you have considered how the cylinder could fit in?

For example, the length of the bottom is 10 and the height is 8, that means the width the bottom is 6. How do you fit in a cylinder with a radius of 5 (i.e., diameter = 10) while the width is only 6?

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in   [#permalink] 05 Dec 2017, 06:34
Display posts from previous: Sort by