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The volume of a box with a square base is 54 cubic centimeters.

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The volume of a box with a square base is 54 cubic centimeters.  [#permalink]

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New post 23 Dec 2018, 09:44
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A
B
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D
E

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Question Stats:

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The volume of a box with a square base is 54 cubic centimeters. If the height of the box is twice the width of the base, what is the height, in centimeters?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

Project PS Butler : Question #95


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Re: The volume of a box with a square base is 54 cubic centimeters.  [#permalink]

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New post 23 Dec 2018, 14:06
Answer is D ie. 6.

Question states that a certain cuboid has a square base.

We know that all the sides in a cube are equal. A cuboid may have unequal sides. The sides are however all perpendicular to each other in both a cuboid as well as a cube. All cubes are hence cuboids but all cuboids are not cubes.

The volume of the cuboid in question is length x breadth x height ie. lbh.

Since the cuboid has a square base, length = breadth. Hence the volume is b x b x h ie. b(sq) x h.

We also know that the height is two times the breadth. Hence the height, h = 2b.

Hence volume, lbh is reduced to 2b(cu) which we know to be equal to 54.

2b(cu) = 54

b = 3

Hence, height h = 6
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Re: The volume of a box with a square base is 54 cubic centimeters.  [#permalink]

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New post 23 Dec 2018, 18:59
given a square base so width = length =x

height = 2x
so 2x^3=54
x=3
height = 6
IMO D

HKD1710 wrote:
The volume of a box with a square base is 54 cubic centimeters. If the height of the box is twice the width of the base, what is the height, in centimeters?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

Project PS Butler : Question #95


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Re: The volume of a box with a square base is 54 cubic centimeters.  [#permalink]

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New post 24 Dec 2018, 14:39
Archit3110 wrote:
given a square base so width = length =x

height = 2x
so 2x^3=54
x=3
height = 6
IMO D



Archit3110 isnt the formula of cuboid vulume - length*width*height

if so, then why are raising to cube power only height ?
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Re: The volume of a box with a square base is 54 cubic centimeters.  [#permalink]

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New post 24 Dec 2018, 21:38
1
dave13 wrote:
Archit3110 wrote:
given a square base so width = length =x

height = 2x
so 2x^3=54
x=3
height = 6
IMO D



Archit3110 isnt the formula of cuboid vulume - length*width*height

if so, then why are raising to cube power only height ?


He hasn't raised height to cube power. He has raised the edge of square to cube power because height is defined in terms of edge of square base.

Check this out!

Here length and width will be equal because the base in square. So let the edge of the base square = s.

volume = length*width*height
54 = (area of base)* height
54 = (s^2) * height

now height is twice the width ==> height = 2s

so, 54= s^2 * 2s
54 = 2 * s^3 ( re-arranging the previous step)

3 = s

height = 2s = 6

KUDOS is this helps! :D
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Re: The volume of a box with a square base is 54 cubic centimeters.  [#permalink]

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New post 25 Dec 2018, 00:38
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dave13

Well I actually missed a step and went direct to the solution :-D

Given in question is that its a square base , so lets take the width of square be x therefore the length would also be x

width=length=x

also given is that the height is twice the width of the base so h= 2x

volume of box would be lengthxbasexheight = 54
or say
x*x*2x=54
x^3=27
x=3

since height is 2x so it would be 2*3 = 6

answer is 6


Hope this helps..

dave13 wrote:
Archit3110 wrote:
given a square base so width = length =x

height = 2x
so 2x^3=54
x=3
height = 6
IMO D



Archit3110 isnt the formula of cuboid vulume - length*width*height

if so, then why are raising to cube power only height ?

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Re: The volume of a box with a square base is 54 cubic centimeters.  [#permalink]

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New post 22 Jan 2019, 00:53
HKD1710 wrote:
The volume of a box with a square base is 54 cubic centimeters. If the height of the box is twice the width of the base, what is the height, in centimeters?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

Project PS Butler : Question #95


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Hello,

Volume of cuboid = L * B * H

L = B = a
H = 2 * B = 2a

Hence:

L * B * H = a * a * 2a = 2a^3 = 54

=> a^=27 i.e a = 3

Now H = 2a = 6

Hence the correct answer is D.
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Re: The volume of a box with a square base is 54 cubic centimeters.   [#permalink] 22 Jan 2019, 00:53
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