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

Question

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

sahibr · Answer

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

Archit3110 · Answer

given a square base so width = length =x

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

dave13 · Answer

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

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

kanakdaga · Answer

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

Archit3110 · Answer

dave13 Well I actually missed a step and went direct to the solution

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..

eabhgoy · Answer

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.

Umaiyer1234 · Answer

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

Slightly different solution

I prime factored 54 54= 3*18=3*6*3
since h=2w and 6 =2*3
h=6

Abhishek009 · Answer

Good method to factorize the number and solve it in seconds, kudos added.

bumpbot · Answer

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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.

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