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## Cube Volumes

Posted by Karl Sharman on June 17, 2010 – 12:13 pm

﻿For any given cuboid it is possible to measure up to three different perimeters.  Given that cuboid A has perimeters 24, 32, and 40, and cuboid B has perimeters 24, 32, and 48, which cuboid has the greatest volume?

Anyone answering “A” or “B” without showing their working out will be deemed to be guessing. No points for guessing!

Karl Sharman

This post is under “MathsChallenge” and has 5 respond so far.

### 5 Responds so far- Add one»

1. 1. John24 Said：

Cuboid A:
perimeter 24 consists of sides with lengths 8,4,8,4
perimeter 32 consists of sides with lengths 12,4,12,4
perimeter 40 consists of sides with lengths 8,12,8,12

Volume = L * W * H
= 12 * 8 * 4
= 384

Cuboid A:
perimeter 24 consists of sides with lengths 10,2,10,2
perimeter 32 consists of sides with lengths 2,14,2,14
perimeter 48 consists of sides with lengths 10,14,10,14

Volume = L * W * H
= 14 * 10 * 2
= 280

Therefore Cuboid A has greatest volume.

Cube has 8 corners and 12 segments. Suppose cube has corners on the front face labelled A, B, C, & D from upper left corner and E, F, G, & H on back face from upper left corner (as viewed from the front)

Cube A Lengths of each segment:
Front Face
AB 8
BC 4
CD 8
DA 4
Left Side
AE 12
EH 4
HD 12
DA 4
Top Side
AE 12
EF 8
FB 12
BA 8

Cube A Lengths of each segment:
Front Face
AB 10
BC 2
CD 10
DA 2
Left Side
AE 14
EH 2
HD 14
DA 2
Top Side
AE 14
EF 10
FB 14
BA 10

2. 2. steev Said：

A < B
24 + 32 + 40 < 24 + 32 + 48

3. 3. Carc Said：

cuboid A’s dimensions are 4, 8 and 12:
2*4+2*8=24, 2*4+2*12=32 and 2*8+2*12=40
it’s easy to calculate this, because you have the three equations a+b=24/2, a+c=32/2 and b+c=40/2
(or just use trial and error)
so cuboid A’s volume is 4*8*12=384

cuboid B’s dimensions are 2, 10 and 14:
2*2+2*10=24, 2*2+2*10=32 and 2*10+2*14=48
so cuboid B’s volume is 2*10*14=280
thus A’s volume is greater than B’s volume

4. 4. Karl Sharman Said：

Well done John24 and Carc. Obviously too easy….

Still, an intersting problem as the obvious response would be that B’s volume is the greater with the gretaer measurements, but not the case as you have proved.

5. 5. lailah Said：

A cube has 6 sides

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